{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "ZyYxarWXICGB"
},
"source": [
" Python en ciencias e ingeniería: tutoriales basados en ejemplos por Sergio Gutiérrez Rodrigo y Adrián Navas Montilla se distribuye bajo una Licencia Creative Commons Atribución-NoComercial-CompartirIgual 4.0 Internacional."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "cU67irCkAoSz"
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"source": [
"---\n",
"Programa de Recursos en Abierto en la UZ (2022)\n",
"\n",
"**Python en ciencias e ingeniería: tutoriales basados en ejemplos**\n",
"---\n",
"Universidad de Zaragoza\n",
"---\n",
"*PRAUZ-739*\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "aZ4I0EbyAqVW"
},
"source": [
"##
Condensador en proceso de carga
\n",
"\n",
"\n",
"-----------------------------------------"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "WV0gKSZ2CGDf"
},
"source": [
"+ El siguiente ejercio no es uno más dentro del Electromagnetismo. Se puede considerar como uno de los problemas *canónicos*, ya que sirve para entender cómo el Electromagnetismo está incompleto si no se incluyen las corrientes de polarización, debidas al genio de J.C. Maxwell.\n",
"+ Al final del notebook se ha incluido unas notas que resumen las ecuaciones de Maxwell."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "29sI19gLJCok"
},
"source": [
"## Enunciado del problema"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "RCNhN-veNbwS"
},
"source": [
"En la figura se muestra el perfil de un condensador de placas plano paralelas, circulares y de radio $a$. El condensador se carga lentamente mediante una corriente $I$.\n",
"+ (a) Obtener la corriente de polarización entre las placas del condensador.\n",
"+ (b) Calcular el campo magnético en todas las regiones del espacio.\n",
"+ (c) Comprobar que se cumplen las condiciones de contorno para el campo magnético en la separación entre regiones. "
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "m1oRcntcJWRb"
},
"source": [
""
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "kKKWFMm1JGDT"
},
"source": [
"## Solución analítica"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "JtmK40RjMCHe"
},
"source": [
"(a) Campo confinado únicamente entre las placas:\n",
"$$ \\mathbf{E}=\\frac{\\sigma_{\\text {cond}}}{\\varepsilon_{0}} \\hat z=\\frac{q}{\\varepsilon_{0} \\pi a^2} \\hat z$$ "
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "70F6ET--MvyS"
},
"source": [
"Deplazamiento eléctrico:\n",
"$$ \\mathbf{D}=\\varepsilon_{0}\\mathbf{E}=\\frac{q}{ \\pi a^2} \\hat z $$ \n"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "aQ0tWkF5NC0D"
},
"source": [
"Si el condensador se carga a ritmo constante mediante una corriente $I=dq/dt$ y asumiendo que la carga se distribuye sobre la superficie de la placa de forma instantánea (razonable si el ritmo de carga es mucho menor que el tiempo de relajación del conductor).\n",
"\n",
"Entoces la corriente de desplazamiento es:\n",
"\n",
"$$ \\mathbf{J}_{\\text{pol}}= \\frac{\\partial}{\\partial t} \\mathbf{D}=\\frac{I}{ \\pi a^2} \\hat z $$ \n",
"\n",
"Siendo la corriente de polarización:\n",
"\n",
"$$I_{\\text{pol}}=\\int_A \\mathbf{J}_{\\text{pol}} \\cdot \\hat n da=\\int_A \\frac{I}{ \\pi a^2} \\hat z \\cdot \\hat n da = I\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "QiwzSOCQQ30y"
},
"source": [
"(b) Cálculo de $\\mathbf{H}(\\mathbf{r}, t)$\n",
"\n",
"Aproximación:\n",
"+ $\\mathbf{H}=H_\\varphi(\\rho) \\hat \\varphi \\rightarrow$ placas circulares y corriente $I$ a lo largo de la dirección $z$\n",
"\n",
"\n",
"Utilizando la ley de Ampère en este caso,\n",
"$$\n",
"\\oint_{C} \\mathbf{H}(\\mathbf{r}, t) \\cdot d \\mathbf{s} =\\int_{A}\\left[\\mathbf{J}(\\mathbf{r}, t)+\\frac{\\partial}{\\partial t} \\mathbf{D}(\\mathbf{r}, t) \\right]\\cdot \\mathbf{n} d a=\\int_A \\left[ \\mathbf{J}_{\\text{cond}}+\\mathbf{J}_{\\text{pol}} \\right]\\cdot \\mathbf{n} d a$$\n",
"intengrando en una trayectoria circular perpendicular de radio $\\rho$ con centro en el eje $z$, se obtiene:\n",
"$$H_\\varphi(\\rho)=\\frac{I_{\\text{pol,enc}}+I_{\\text{cond,enc}}}{2\\pi \\rho}$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "UNu-IThrYiEY"
},
"source": [
"Si dividimos el espacio en las siguientes regiones "
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "A48I1NdWJS8j"
},
"source": [
""
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "3qKWe6osRYcp"
},
"source": [
"entonces los resultados son:\n",
"\n",
"**Región 3 y 4** \n",
"\n",
"$I_{\\text{pol,enc}}=0$ y $I_{\\text{cond,enc}}=I \\rightarrow$ $H_\\varphi(\\rho)=\\frac{I}{2\\pi \\rho}$\n",
"\n",
"**Región 2** \n",
"\n",
"$I_{\\text{pol,enc}}=I_{\\text{pol}}=I$ y $I_{\\text{cond}}=0 \\rightarrow$ $H_\\varphi(\\rho)=\\frac{I}{2\\pi \\rho} (\\rho > a)$\n",
"\n",
"\n",
"**Región 1** \n",
"\n",
"$I_{\\text{cond}}=0$ y $I_{\\text{pol,enc}}/I_{\\text{pol}}=I_{\\text{pol,enc}}/I=\\pi \\rho^2/\\pi a^2=\\rho^2/a^2 \\rightarrow$ $H_\\varphi(\\rho)=\\frac{I \\rho}{2\\pi a^2} (\\rho \\le a)$"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "90noy1MVXVPF"
},
"source": [
"c) Según las condiciones de contorno para el campo magnético\n",
"\n",
"$\\hat n \\times (\\mathbf{H}_2-\\mathbf{H}_1)=\\mathbf{K}$ o ${H}_{2t}-H_{1t}=\\mathbf{K} \\times \\hat n $\n",
"\n",
"Aquí la componente tangencial es $H_{t}=H_\\varphi(\\rho)$\n",
"\n",
"+ Entre las regiones 3 y 2 y 2 y 4 la corriente superficial de carga es cero y por lo tanto el campo mágnetico es continuo. \n",
"+ Entre las regiones 1 y 3 (1 y 4) la corriente superficial de carga no es cero. \n",
"+ Para hacer el cálculo podemos suponer que la carga se distribuye instantáneamente y de forma uniforme en las placas. \n",
"+ Por simetría $\\mathbf{K}$ debe ser radial, $\\mathbf{K}=K(\\rho) \\hat \\rho$, como se representa en la figura de abajo.\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "mPZ4xp-FbYXS"
},
"source": [
""
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "Vfo1L-ZfbbWC"
},
"source": [
"+ El flujo de carga ($C/s$) que entra a través de la superficie delimitada por $\\rho$ es $\\Phi_S=\\int K da=2 \\pi \\rho K$\n",
"+ En un instante $\\Delta t$ la carga que entra y se distribuye en las placas debe ser:\n",
" - por un lado $2 \\pi \\rho K \\Delta t$ \n",
" - por el otro $\\Delta\\sigma (\\pi a^2 - \\pi \\rho^2)=\\frac{\\Delta q}{\\pi a^2}(\\pi a^2 - \\pi \\rho^2)=I \\Delta t(1 - \\rho^2/a^2)$, ya que $\\Delta q=I \\Delta t$\n",
"+ De igualar estas expresiones se obtiene que \n",
"\n",
"$$K(\\rho)=\\frac{I}{2\\pi \\rho} (1 - \\rho^2/a^2)$$\n",
"\n",
"+ Como $\\hat \\rho \\times \\hat z =- \\hat \\varphi$ y $\\vert {H}_{1}-H_{3} \\vert=K(\\rho)$ se cumplen las condiciones de contorno"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "jlIv0Im2JlXL"
},
"source": [
"## Representación gráfica"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "fwlKQhXfL6MK"
},
"source": [
"### Funciones auxiliares para representación gráfica"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "CEj0Xj83fSK8"
},
"outputs": [],
"source": [
"import warnings\n",
"warnings.filterwarnings(\"ignore\")\n",
"\n",
"import matplotlib.pyplot as plt\n",
"from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
"import numpy as np\n",
"from math import pi\n",
"\n",
"def plot_field_radial(field,Rcore_ini,Rcore_fin,Rmax=10.0): \n",
" N=300\n",
" R_core_l1 = np.linspace(Rcore_ini,Rcore_fin , N)\n",
" R_core_l2 = np.linspace(-Rcore_ini,-Rcore_fin , N)\n",
" R_cladding_l1=np.linspace(Rcore_fin, Rmax, N)\n",
" R_cladding_l2=np.linspace(-Rcore_fin,-Rmax, N)\n",
" from numpy import pi\n",
" xcore1=R_core_l1\n",
" xcore2=R_core_l2\n",
" xcladding1=R_cladding_l1\n",
" xcladding2=R_cladding_l2\n",
" ycore1=np.abs(field(xcore1,pi/4.0))\n",
" ycore2=np.abs(field(xcore2,pi/4.0))\n",
" ycladding=np.abs(field(xcladding1,pi/4.0))\n",
" \n",
" # Along a given direction\n",
" fig, ax = plt.subplots(figsize=(4,4))\n",
" ax.plot(xcore1,ycore1)\n",
" ax.plot(xcore2,ycore2)\n",
" ax.plot(xcladding1,ycladding)\n",
" ax.plot(xcladding2,ycladding)\n",
" ax.set_xlabel(r'$\\rho$') \n",
" plt.rc('lines',marker='o', linewidth=0.5, markersize=1)\n",
" plt.show() \n",
" pass\n",
"\n",
"def plot_field_polar(field_func,Rcore_ini,Rcore_fin,Rmax=10.0): \n",
" # Using linspace so that the endpoint of 360 is included\n",
" N=300\n",
" phi_core_l = np.radians(np.linspace(0, 360, N))\n",
" R_core_l = np.linspace(Rcore_ini, Rcore_fin, N)\n",
" phi_cladding_l = np.radians(np.linspace(0, 360, N))\n",
" R_cladding_l = np.linspace(Rcore_fin, Rmax, N)\n",
" # Creates a mesh (R,phi)\n",
" R_core, phi_core = np.meshgrid(R_core_l, phi_core_l)\n",
" R_cladding, phi_cladding = np.meshgrid(R_cladding_l, phi_cladding_l) \n",
" \n",
" #Field(R,phi) \n",
" core = field_func(R_core,phi_core)\n",
" cladding= field_func(R_cladding,phi_cladding)\n",
" vmaxcore=np.max(np.abs(core))\n",
" vmaxcladding=np.max(np.abs(cladding)) \n",
" field_max=max(vmaxcore,vmaxcladding)\n",
" \n",
" R=np.hstack((R_core,R_cladding)) \n",
" phi=np.hstack((phi_core,phi_cladding)) \n",
" field=np.hstack((core,cladding))\n",
" print(np.max(field))\n",
" #Plot\n",
" print(\"max=\",field_max)\n",
" fig, ax = plt.subplots(figsize=(3,3),dpi=100,\n",
" subplot_kw=dict(projection='polar'))\n",
" img=ax.contourf(phi, R,field,cmap='bwr') \n",
" ax.set_theta_offset(pi/2.0)\n",
" ax.set_title(field_func.__name__,loc= 'left') \n",
" plt.colorbar(img)\n",
" plt.show() \n",
" pass \n",
"\n",
"def plot_field_vector(field,Rcore_ini,Rcore_fin):\n",
" import numpy as np\n",
" from matplotlib import pyplot as plt\n",
" plt.rcParams[\"figure.figsize\"] = [7.50, 3.50]\n",
" plt.rcParams[\"figure.autolayout\"] = True\n",
" radii = np.linspace(Rcore_ini, Rcore_fin, 4)\n",
" thetas = np.linspace(0, 2 * np.pi, 12)\n",
" theta, r = np.meshgrid(thetas, radii) \n",
" f = plt.figure()\n",
" #Componentes polares\n",
" urho,uphi=field(r,theta) \n",
" # Componentes cartesianas\n",
" ux=urho*np.cos(theta)-uphi*np.sin(theta)\n",
" uy=urho*np.sin(theta)+uphi*np.cos(theta)\n",
" #ux=ux/np.sqrt(ux**2+uy**2)\n",
" #uy=uy/np.sqrt(ux**2+uy**2)\n",
"\n",
" ax = f.add_subplot(polar=True)\n",
" ax.quiver(theta, r, ux,uy) # Hay que pasarle coordenadas en polares pero\n",
" # vector en cartesianas\n",
" plt.show() \n",
" pass"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "myVjzCB4L-u5"
},
"source": [
"### Definición de funciones: $H_\\varphi(\\rho)$, $\\mathbf{K}=K(\\rho) \\hat \\rho$ y condiciones de contorno"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "8PQugkAWiZlw"
},
"outputs": [],
"source": [
"import numpy as np\n",
"from math import pi \n",
"# Parámetros del ejercicio\n",
"a= 0.1 # metros\n",
"I= 0.1 # A\n",
"\n",
"# H región 1 y 2\n",
"def H12(r,phi): \n",
" if(np.max(r)<=a):\n",
" return I*r/(2.0*pi*a**2)\n",
" else:\n",
" return I/(2.0*pi*r)\n",
"\n",
"# H región 3 y 4 \n",
"def H34(r,phi): \n",
" return I/(2.0*pi*r)\n",
"\n",
"# Corriente superficial de carga K\n",
"def K(r,phi):\n",
" rho=I*(1.0-(r/a)**2)/(2.0*pi*r)\n",
" phi=0.0\n",
" return rho,phi\n",
"\n",
"# Corriente superficial de carga K (componente radial)\n",
"def kr(r,phi):\n",
" urho,uphi=K(r,phi)\n",
" return urho\n",
"\n",
"# Condiciones de contorno entre región 1-3 y 2-3\n",
"def cond_contorno(r,phi):\n",
" return H12(r,phi)-H34(r,phi)\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "LsT2dmAvj-_T"
},
"source": [
"### Representación polar de $H_\\varphi(\\rho)$ (región 1 y 2)."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 623
},
"executionInfo": {
"elapsed": 1620,
"status": "ok",
"timestamp": 1661856744718,
"user": {
"displayName": "SERGIO GUTIERREZ RODRIGO",
"userId": "07959720391705098820"
},
"user_tz": -120
},
"id": "2SsagLxuj_ni",
"outputId": "0ed3dbc2-e9a5-4386-a32d-179af1db4f59"
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"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.15915494309189535\n",
"max= 0.15915494309189535\n"
]
},
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"max_field=plot_field_polar(H12,Rcore_ini=0.0,Rcore_fin=a,Rmax=3.0*a)\n",
"plot_field_radial(H12,Rcore_ini=0.0,Rcore_fin=a,Rmax=2.0*a)"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "CHGeLS4HMNoM"
},
"source": [
"### Representación polar de $H_\\varphi(\\rho)$ (región 3 o 4)."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 659
},
"executionInfo": {
"elapsed": 632,
"status": "ok",
"timestamp": 1661856745348,
"user": {
"displayName": "SERGIO GUTIERREZ RODRIGO",
"userId": "07959720391705098820"
},
"user_tz": -120
},
"id": "MkyVNnPY5r4z",
"outputId": "5ea3ede2-1111-4bb0-f11f-67239cec9742"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"15.915494309189533\n",
"max= 15.915494309189533\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:16: RuntimeWarning: divide by zero encountered in true_divide\n",
" app.launch_new_instance()\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"max_field=plot_field_polar(H34,Rcore_ini=0.01*a,Rcore_fin=a,Rmax=3.0*a)\n",
"plot_field_radial(H34,Rcore_ini=0.0,Rcore_fin=a,Rmax=2.0*a)"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "HDrVlHaYM4E5"
},
"source": [
"### Condiciones de contorno: $H_1 - H_3$ vs $H_2 - H_3$, en función de $\\rho$."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 677
},
"executionInfo": {
"elapsed": 909,
"status": "ok",
"timestamp": 1661856747622,
"user": {
"displayName": "SERGIO GUTIERREZ RODRIGO",
"userId": "07959720391705098820"
},
"user_tz": -120
},
"id": "NY24S5YzM4Nx",
"outputId": "3a51284a-9e7e-4914-cc52-93c5eab8e850"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.0\n",
"max= 0.7639437268410976\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"H12-H34\n",
"rho <= a -0.238732414637843\n",
"rho > a 0.0\n"
]
}
],
"source": [
"plot_field_polar(cond_contorno,Rcore_ini=0.2*a,Rcore_fin=a,Rmax=2.0*a)\n",
"plot_field_radial(cond_contorno,Rcore_ini=0.2*a,Rcore_fin=a,Rmax=2.0*a)\n",
"\n",
"print(\"H12-H34\")\n",
"print('rho <= a',H12(r=0.5*a,phi=0.0)-H34(r=0.5*a,phi=0.0))\n",
"print('rho > a',H12(r=2.0*a,phi=0.0)-H34(r=2.0*a,phi=0.0))"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "e8VfWunmiX3C"
},
"source": [
"### Corriente superficial de carga $\\mathbf{K}=K(\\rho) \\hat \\rho$"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 541
},
"executionInfo": {
"elapsed": 1150,
"status": "ok",
"timestamp": 1661856910096,
"user": {
"displayName": "SERGIO GUTIERREZ RODRIGO",
"userId": "07959720391705098820"
},
"user_tz": -120
},
"id": "Ax5sDe72gPc5",
"outputId": "7a428aa3-540e-41ed-fb64-65b358a5d425"
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plot_field_vector(K,Rcore_ini=0.3*a,Rcore_fin=a)\n",
"plot_field_radial(kr,Rcore_ini=0.04*a,Rcore_fin=a,Rmax=1.0*a)"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "B8mgI7rKiaKy"
},
"source": [
"# Repaso de las ecuaciones de Maxwell"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "HdtqqUVwiPmZ"
},
"source": [
"## Electromagnetismo microscópico y macroscópico"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "9hk76edlifvp"
},
"source": [
"\n",
"Densidad de carga $\\rho$ y densidad de corriente $\\mathbf{J}$ :\n",
"$$\n",
"\\begin{aligned}\n",
"&\\rho(\\mathbf{r})=\\sum_{\\mathrm{n}} \\mathrm{q}_{\\mathrm{n}} \\delta\\left[\\mathbf{r}-\\mathbf{r}_{\\mathrm{n}}\\right] \\\\\n",
"&\\mathbf{J}(\\mathbf{r})=\\sum_{\\mathrm{n}} \\mathrm{q}_{\\mathrm{n}} \\dot{\\mathrm{r}}_{\\mathrm{n}} \\delta\\left[\\mathbf{r}-\\mathbf{r}_{\\mathrm{n}}\\right]\n",
"\\end{aligned}\n",
"$$\n",
"En función de las cargas discretas $\\mathrm{q}_{\\mathrm{i}}$, en la posición $\\mathbf{r}_{\\mathrm{n}}$.\n",
"\n",
"*$\\mathbf{r}_{\\mathrm{n}}$ = vector de posición de la $n$th carga y $\\dot{\\mathbf{r}}_{\\mathrm{n}}=\\mathbf{v}_{\\mathrm{n}}$ su velocidad.* \n",
"\n",
"La fuerza de Lorentz queda, tras integrar:\n",
"$$\n",
"\\mathbf{F}(\\mathbf{r}, t)=\\int_{V}[\\rho(\\mathbf{r}, t) \\mathbf{E}(\\mathbf{r}, t)+\\mathbf{J}(\\mathbf{r}, t) \\times \\mathbf{B}(\\mathbf{r}, t)] \\mathrm{d} V\n",
"$$\n",
"siendo $V$ el volumen que contiene todas las cargas $q_{\\mathrm{n}}$.\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "6gIe0N9omjbU"
},
"source": [
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "q7B-y3bWyEva"
},
"source": [
"## Electrodinámica *pre-Maxwelliana*"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "Y6ynpoRpi8PJ"
},
"source": [
"Ecuaciones \"pre-Maxwellianas\"\n",
"$$\n",
"\\begin{array}{l}\n",
"\\oint_{A} \\mathbf{E}(\\mathbf{r}, t) \\cdot \\mathbf{n} d a=\\frac{1}{\\varepsilon_{0}} \\int_{V} \\rho(\\mathbf{r}, t) d V & \\text {Ley de Gauss (Cavendish 1772) } \\\\\n",
"\\oint_{C} \\mathbf{E}(\\mathbf{r}, t) \\cdot d \\mathbf{s}=-\\frac{\\partial}{\\partial t} \\int_{A} \\mathbf{B}(\\mathbf{r}, t) \\cdot \\mathbf{n} d a & \\text { Ley de Faraday (Faraday 1825) } \\\\\n",
"\\oint_{C} \\mathbf{B}(\\mathbf{r}, t) \\cdot d \\mathbf{s}=\\mu_{0} \\int_{A} \\mathbf{J}(\\mathbf{r}, t) \\cdot \\mathbf{n} d a & \\text { Ley de Ampère (Oersted 1819) } \\\\\n",
"\\oint_{A} \\mathbf{B}(\\mathbf{r}, t) \\cdot \\mathbf{n} d a=0 & \\text { }\n",
"\\end{array}\n",
"$$\n",
"\n",
"+ $V$ es el volumen compuesto de elementos $d V$.\n",
"+ $A$ es la superficie compuesta por elementos diferenciales $da$.\n",
"+ $C$ la circulación a lo largo del perímetro de la superficie abierta $A$.\n",
"+ $d \\mathbf{s}$ es un elemento infinitesimal de línea. \n",
"+ $\\mathbf{n}$ es el vector unitario normal a $A$. \n",
"\n",
"Las constantes son:\n",
"$$\n",
"\\begin{aligned}\n",
"&\\mu_{0}=4 \\pi 10^{-7} \\frac{\\mathrm{Vs}}{\\mathrm{Am}}=1.256637010^{-6} \\frac{\\mathrm{Vs}}{\\mathrm{Am}} \\text { (permeabilidad magnética) } \\\\\n",
"&\\varepsilon_{0}=8.854187810^{-12} \\frac{\\mathrm{As}}{\\mathrm{Vm}} \\text { (permitividad eléctrica) }\n",
"\\end{aligned}\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "zMktveFzivdF"
},
"source": [
""
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "na0ElW4dv28F"
},
"source": [
"Leyes de Kirchhoff a partir de las ecuaciones de Maxwell. La base de la teoría de circuitos y el diseño electrónico.\n",
"\n",
"- Consideremos la ley de Ampère en las caras de un cubo arbitrariamente pequeño.\n",
"- $\\oint_{C} \\mathbf{B}(\\mathbf{r}, t) \\cdot d \\mathbf{s}$ en caras opuestas tienen aprox. el mismo valor pero con signo contrario.\n",
"- La suma de las circulaciones de cada par de caras enfrentadas es cero.\n",
"\n",
"Por lo tanto:\n",
"$$\n",
"\\oint_{A} \\mathbf{J}(\\mathbf{r}, t) \\cdot \\mathbf{n} d a=0 \\quad \\text { }\n",
"$$\n",
"\n",
"- Lo mismo ocurre con la ley de Faraday, $\\oint_{C} \\mathbf{E}(\\mathbf{r}, t) \\cdot d \\mathbf{s}$, si no existen campos magnéticos dependientes del tiempo.\n",
"\n",
"En este caso\n",
"$$\n",
"\\oint_{C} \\mathbf{E}(\\mathbf{r}, t) \\cdot d \\mathbf{s}=0 \\quad\n",
"$$\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "l2p3cCcFi2uU"
},
"source": [
""
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "4aPGuD95jhfE"
},
"source": [
"## Corriente de desplazamiento\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "3bVtor0pjHcx"
},
"source": [
""
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "s431GVdTjH8D"
},
"source": [
"Cuando el campo électrico cambia con el tiempo lo expresado en el apartado lleva a una contradicción, como demuestra el experimento meental de arriaba:\n",
"$$\n",
"\\oint_{A} \\mathbf{J}(\\mathbf{r}, t) \\cdot \\mathbf{n} d a \\neq 0\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "vbNmbTrzjbc1"
},
"source": [
"Corrección conservación de corriente:\n",
"$$\n",
"\\oint_{A} \\mathbf{J}(\\mathbf{r}, t) \\cdot \\mathbf{n} d a=-\\frac{\\partial}{\\partial t} \\int_{V} \\rho(\\mathbf{r}, t) d V\n",
"$$\n",
"\n",
"Maxwell modificó la ley de Ampère añadiendo un nuevo término\n",
"$$\n",
"\\oint_{C} \\mathbf{B}(\\mathbf{r}, t) \\cdot d \\mathbf{s}=\\mu_{0} \\int_{A} \\mathbf{J}(\\mathbf{r}, t) \\cdot \\mathbf{n} d a+\\varepsilon_{0} \\mu_{0} \\frac{\\partial}{\\partial t} \\int_{A} \\mathbf{E}(\\mathbf{r}, t) \\cdot \\mathbf{n} d a\n",
"$$\n",
"\n",
"Donde se define la corriente de desplazamiento como:\n",
"$$\\varepsilon_{0} \\partial \\mathbf{E} / \\partial t$$\n",
"\n",
"Repitiendo el ejercicio mental previo, integrando sobre un cubo diferencial obtenemos:\n",
"$$\n",
"\\mu_{0} \\oint_{A} \\mathbf{J}(\\mathbf{r}, t) \\cdot \\mathbf{n} d a+\\varepsilon_{0} \\mu_{0} \\frac{\\partial}{\\partial t} \\oint_{A} \\mathbf{E}(\\mathbf{r}, t) \\cdot \\mathbf{n} d a=0 .\n",
"$$\n",
"\n",
"Pero como $$\\oint_{A} \\mathbf{E}(\\mathbf{r}, t) \\cdot \\mathbf{n} d a=\\frac{1}{\\varepsilon_{0}} \\int_{V} \\rho(\\mathbf{r}, t) d V$$\n",
"\n",
"Y por lo tanto:\n",
"\n",
"$$\n",
"\\begin{array}{}\n",
"\\oint_{A} \\mathbf{E}(\\mathbf{r}, t) \\cdot \\mathbf{n} d a=\\frac{1}{\\varepsilon_{0}} \\int_{V} \\rho(\\mathbf{r}, t) d V \\\\\n",
"\\oint_{C} \\mathbf{E}(\\mathbf{r}, t) \\cdot d \\mathbf{s}=-\\frac{\\partial}{\\partial t} \\int_{A} \\mathbf{B}(\\mathbf{r}, t) \\cdot \\mathbf{n} d a\\\\\n",
"\\oint_{C} \\mathbf{B}(\\mathbf{r}, t) \\cdot d \\mathbf{s}=\\mu_{0} \\int_{A} \\mathbf{J}(\\mathbf{r}, t) \\cdot \\mathbf{n} d a+\\varepsilon_{0} \\mu_{0} \\frac{\\partial}{\\partial t} \\int_{A} \\mathbf{E}(\\mathbf{r}, t) \\cdot \\mathbf{n} d a \\\\\n",
"\\oint_{A} \\mathbf{B}(\\mathbf{r}, t) \\cdot \\mathbf{n} d a=0 \n",
"\\end{array}\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "lDxud_l-NCL3"
},
"source": []
},
{
"cell_type": "markdown",
"metadata": {
"id": "zqLrg50mkGXd"
},
"source": [
"## Interacción entre los campos EM y la materia"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "kSm_lJRpjpfc"
},
"source": [
"Hasta el momento hemos discutido las propiedades de los campos EM $\\mathbf{E}$ y $\\mathbf{B}$ en vacío. \n",
"+ Las fuentes de estos campos son las cargas $\\rho$ y corrientes $\\mathbf{J}$ (fuentes primarias). \n",
"+ $\\mathbf{E}$ y $\\mathbf{B}$ pueden interactuar con los materiales dando lugar a cargas y corrientes inducidas (fuentes secundarias).\n",
"\n",
"Las fuentes secundarias las podemos introducir como:\n",
"$$\n",
"\\rho_{\\mathrm{tot}}=\\rho+\\rho_{\\mathrm{pol}}\n",
"$$\n",
"\n",
"+ $\\rho$ es la carga asociada con las fuentes primarias. \n",
"+ Se asume que estas fuentes no se ven afectadas por los campos $\\mathbf{E}$ y $\\mathbf{B}$. \n",
"+ $\\rho_{\\text {pol }}$ es la densidad de carga inducida en la materia por interacción con el campo eléctrico (densidad de carga de polarización)\n",
"\n",
"Se introduce el vector polarización $\\mathbf{P}$ para tener en cuenta a $\\rho_{\\text {pol }}$. Por analogía con la ley de Gauss:\n",
"$$\n",
"\\oint_{A} \\mathbf{P}(\\mathbf{r}, t) \\cdot \\mathbf{n} d a=-\\int_{V} \\rho_{\\mathrm{pol}}(\\mathbf{r}, t) d V\n",
"$$\n",
"[$\\mathbf{P}$]=$\\mathrm{C} / \\mathrm{m}^{2}$."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "ioE1OIEwx8xy"
},
"source": [
"Insertando las expresiones anteriores en la ley de Gauss\n",
"$$\\oint_{A} \\mathbf{E}(\\mathbf{r}, t) \\cdot \\mathbf{n} d a=\\frac{1}{\\varepsilon_{0}} \\int_{V} \\rho_{tot}(\\mathbf{r}, t) d V \n",
"$$\n",
"se obtiene:\n",
"$$\n",
"\\oint_{A}\\left[\\varepsilon_{0} \\mathbf{E}(\\mathbf{r}, t)+\\mathbf{P}(\\mathbf{r}, t)\\right] \\cdot \\mathbf{n} d a=\\int_{V} \\rho(\\mathbf{r}, t) d V\n",
"$$\n",
"La expresión entre corchetes es el desplazamiento eléctrico:\n",
"$$\n",
"\\mathbf{D}=\\varepsilon_{0} \\mathbf{E}+\\mathbf{P} \n",
"$$\n",
"\n",
"La variación temporal de las densidad de carga da lugar a corrientes de polarización. \n",
"$$\n",
"\\oint_{A} \\frac{\\partial}{\\partial t} \\mathbf{P}(\\mathbf{r}, t) \\cdot \\mathbf{n} d a=-\\frac{\\partial}{\\partial t} \\int_{V} \\rho_{\\mathrm{pol}}(\\mathbf{r}, t) d V,\n",
"$$\n",
"Si la comparamos con la ecuación de conservación de la corriente,\n",
"$$\n",
"\\oint_{A} \\mathbf{J}(\\mathbf{r}, t) \\cdot \\mathbf{n} d a=-\\frac{\\partial}{\\partial t} \\int_{V} \\rho(\\mathbf{r}, t) d V\n",
"$$\n",
"\n",
"se identifica $\\partial \\mathbf{P} / \\partial t$ como la corriente de polarización del material. \n",
"$$\n",
"\\mathbf{J}_{\\mathrm{pol}}(\\mathbf{r}, t)=\\frac{\\partial}{\\partial t} \\mathbf{P}(\\mathbf{r}, t) \n",
"$$\n",
"\n",
"La dinámica de las fuentes secundarias de polarización depende de las propiedades materiales:$[\\mathbf{P}=f(\\mathbf{E})]$.\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "LZT8OxCl1agh"
},
"source": [
"La densidad de corriente debe incluir también corrientes debidas a cargas libres, $\\mathrm{J}_{\\text {cond }}$. Entonces:\n",
"$$\n",
"\\mathbf{J}_{\\text {tot }}(\\mathbf{r}, t)=\\mathbf{J}_{0}(\\mathbf{r}, t)+\\mathbf{J}_{\\text {cond }}(\\mathbf{r}, t)+\\mathbf{J}_{\\mathrm{pol}}(\\mathbf{r}, t)+\\mathbf{J}_{\\mathrm{mag}}(\\mathbf{r}, t)\n",
"$$\n",
"donde $\\mathbf{J}_{0}$ es la densidad de corriente de las fuentes de campo EM. \n",
"Para simplificar se define:\n",
"$$\n",
"\\mathbf{J}(\\mathbf{r}, t)=\\mathbf{J}_{0}(\\mathbf{r}, t)+\\mathbf{J}_{\\text {cond }}(\\mathbf{r}, t) \n",
"$$\n",
"De esta forma:\n",
"+ $\\mathbf{J}$ es la densidad de corriente de las cargas libres (sin importar su origen).\n",
"+ $\\mathbf{J}_{\\mathrm{pol}}$ es la densidad de corriente de las cargas ligadas, cargas que experimentan fuerzas centrales. \n",
"+$\\mathbf{J}_{\\mathrm{mag}}$ es la densidad de corriente debida a cargas \"circulantes\", asociadas a momentos magnéticos.\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "NSWVBdfDzl8S"
},
"source": [
"\n",
"Introduciendo las corrientes \n",
"$$\n",
"\\mathbf{J}_{\\text {tot }}(\\mathbf{r}, t)=\\mathbf{J}(\\mathbf{r}, t)+\\mathbf{J}_{\\mathrm{pol}}(\\mathbf{r}, t)+\\mathbf{J}_{\\mathrm{mag}}(\\mathbf{r}, t)\n",
"$$\n",
"\n",
"en la ley de Ampère\n",
"$$\n",
"\\oint_{C} \\mathbf{B}(\\mathbf{r}, t) \\cdot d \\mathbf{s}=\\mu_{0} \\int_{A} \\mathbf{J}_{\\text {tot }}(\\mathbf{r}, t) \\cdot \\mathbf{n} d a+\\varepsilon_{0} \\mu_{0} \\frac{\\partial}{\\partial t} \\int_{A} \\mathbf{E}(\\mathbf{r}, t) \\cdot \\mathbf{n} d a\n",
"$$\n",
"se obtiene:\n",
"$$\n",
"\\oint_{C} \\mathbf{B} \\cdot d \\mathbf{s}=\\mu_{0} \\int_{A}\\left[\\mathbf{J}+\\left(\\mathbf{J}_{\\mathrm{pol}}+\\varepsilon_{0} \\frac{\\partial}{\\partial t} \\mathbf{E}\\right)+\\mathbf{J}_{\\mathrm{mag}}\\right] \\cdot \\mathbf{n} d a\n",
"$$\n",
"\n",
"Si tenemos en cuenta que: \n",
"+ $\\partial \\mathbf{D} / \\partial t=\\mathbf{J}_{\\mathrm{pol}}+\\varepsilon_{0} \\frac{\\partial}{\\partial t} \\mathbf{E}$\n",
"+ La magnetización inducida se puede escribir como:\n",
"$\n",
"\\oint_{C} \\mathbf{M}(\\mathbf{r}, t) \\cdot d \\mathbf{s}=\\int_{A} \\mathbf{J}_{\\operatorname{mag}}(\\mathbf{r}, t) \\cdot \\mathbf{n} d a\n",
"$\n",
"siendo $\\mathrm{M}$ la magnetización, se obtiene que:\n",
"\n",
"$$\n",
"\\oint_{C}\\left[\\frac{1}{\\mu_{0}} \\mathbf{B}-\\mathbf{M}\\right] \\cdot d \\mathbf{s}=\\int_{A}\\left[\\mathbf{J}+\\frac{\\partial}{\\partial t} \\mathbf{D}\\right] \\cdot \\mathbf{n} d a\n",
"$$\n",
"\n",
"Se define el campo magnético como:\n",
"$$\n",
"\\mathbf{H}=\\frac{1}{\\mu_{0}} \\mathbf{B}-\\mathbf{M}\n",
"$$\n",
"que tiene unidades de $A / m$. \n",
"\n",
"La magnitud y la dinámica de las corrientes de magnetización dependen de las propiedades del material $[\\mathbf{M}=f(\\mathbf{B})]$.\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "cylPnXop_U6K"
},
"source": [
"## Ecuaciones de Maxwell en su forma general"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "YtXrtVkB8F7e"
},
"source": [
"Las ecuaciones de Maxwell en su forma integral quedan como:\n",
"\n",
"$$\n",
"\\begin{aligned}\n",
"\\oint_{A} \\mathbf{D}(\\mathbf{r}, t) \\cdot \\mathbf{n} d a &=\\int_{V} \\rho(\\mathbf{r}, t) d V \\\\\n",
"\\oint_{C} \\mathbf{E}(\\mathbf{r}, t) \\cdot d \\mathbf{s} &=-\\frac{\\partial}{\\partial t} \\int_{A} \\mathbf{B}(\\mathbf{r}, t) \\cdot \\mathbf{n} d a \\\\\n",
"\\oint_{C} \\mathbf{H}(\\mathbf{r}, t) \\cdot d \\mathbf{s} &=\\int_{A}\\left[\\mathbf{J}(\\mathbf{r}, t)+\\frac{\\partial}{\\partial t} \\mathbf{D}(\\mathbf{r}, t)\\right]\\cdot \\mathbf{n} d a \\\\\n",
"\\oint_{A} \\mathbf{B}(\\mathbf{r}, t) \\cdot \\mathbf{n} d a &=0\n",
"\\end{aligned}\n",
"$$\n",
"\n",
"El desplazamiento eléctrico $\\mathrm{D}$ y la inducción magnética $\\mathbf{B}$ dan cuenta de las fuentes secundarias a través de las siguientes expresiones:\n",
"\n",
"$$\n",
"\\mathbf{D}(\\mathbf{r}, t)=\\varepsilon_{0} \\mathbf{E}(\\mathbf{r}, t)+\\mathbf{P}(\\mathbf{r}, t), \\quad \\mathbf{B}(\\mathbf{r}, t)=\\mu_{0}[\\mathbf{H}(\\mathbf{r}, t)+\\mathbf{M}(\\mathbf{r}, t)]\n",
"$$\n",
"\n",
"+ Son válidas siempre ya que no se han hayado para un material particular. \n",
"+ Para resolver las ecuaciones de Maxwell es necesario determinar las propiedades materiales codificadas en $\\mathbf{P}$ y $\\mathbf{M}$, llamadas relaciones constitutivas. En la mayoría de los materiales esta relación viene dada como: $\\mathbf{P}=f(\\mathbf{E})$ and $\\mathbf{M}=f(\\mathbf{B})$ (excepciones: p.ej. materiales bi-isotrópicos)."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "YfAQnj9SkAI7"
},
"source": [
"Mediante los teoremas de Stokes y Gauss se pueden reescribir las ecuaciones de Maxwell en su forma diferencial.\n",
"\n",
"$$\n",
"\\begin{aligned}\n",
"\\oint_{A} \\mathbf{F}(\\mathbf{r}, t) \\cdot \\mathbf{n} d a &=\\int_{V} \\nabla \\cdot \\mathbf{F}(\\mathbf{r}, t) d V \\quad \\text { Teorema de Gauss} \\\\\n",
"\\oint_{C} \\mathbf{F}(\\mathbf{r}, t) \\cdot d \\mathbf{s} &=\\int_{A}[\\nabla \\times \\mathbf{F}(\\mathbf{r}, t)] \\cdot \\mathbf{n} d a \\quad \\text { Teorema de Stokes }\n",
"\\end{aligned}\n",
"$$\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "AXEJHnuLkOc7"
},
"source": [
"Por ejemplo, aplicando el teorema de Gauss a la primera integral queda\n",
"\n",
"$$\n",
"\\int_{V}[\\nabla \\cdot \\mathbf{D}(\\mathbf{r}, t)-\\rho(\\mathbf{r}, t)] d V=0\n",
"$$\n",
"\n",
"El resultado debe ser válido para cualquier volumen $V$. Eso solo es posible si el integrando es cero, esto es,\n",
"\n",
"$$\n",
"\\nabla \\cdot \\mathbf{D}(\\mathbf{r}, t)=\\rho(\\mathbf{r}, t)\n",
"$$\n",
"\n",
"$$\n",
"\\begin{aligned}\n",
"\\nabla \\cdot \\mathbf{D}(\\mathbf{r}, t) &=\\rho(\\mathbf{r}, t) \\\\\n",
"\\nabla \\times \\mathbf{E}(\\mathbf{r}, t) &=-\\frac{\\partial}{\\partial t} \\mathbf{B}(\\mathbf{r}, t) \\\\\n",
"\\nabla \\times \\mathbf{H}(\\mathbf{r}, t) &=\\frac{\\partial}{\\partial t} \\mathbf{D}(\\mathbf{r}, t)+ \\mathbf{J}(\\mathbf{r}, t)\\\\\n",
"\\nabla \\cdot \\mathbf{B}(\\mathbf{r}, t) &=0\n",
"\\end{aligned}\n",
"$$\n",
"\n",
"La ley de conservación de la carga está continuidad implícitamente en las ecuaciones de Maxwell.\n",
"\n",
"Tomando la divergencia de \n",
"$$\n",
"\\begin{aligned}\n",
"\\nabla \\times \\mathbf{H}(\\mathbf{r}, t) =\\frac{\\partial}{\\partial t} \\mathbf{D}(\\mathbf{r}, t)+ \\mathbf{J}(\\mathbf{r}, t)\n",
"\\end{aligned}\n",
"$$\n",
"\n",
"+ sabiendo que $\\nabla \\cdot \\nabla \\times \\mathrm{H}=0$ \n",
"+ $\\nabla \\cdot \\mathbf{D}(\\mathbf{r}, t) =\\rho(\\mathbf{r}, t) $\n",
"\n",
"Se obtiene la ecuación de continuidad \n",
"$$\n",
"\\nabla \\cdot \\mathbf{J}(\\mathbf{r}, t)+\\frac{\\partial}{\\partial t} \\rho(\\mathbf{r}, t)=0\n",
"$$\n",
"consistente con la forma integral derivada previamente."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "Eci8GVxzTutZ"
},
"source": [
"Las condiciones de frontera se pueden obtener utilizando las ecuaciones de Maxwell (están contenidas en ellas):\n",
"\n",
"$$\n",
"\\begin{aligned}\n",
"\\hat n \\cdot (\\mathbf{D}_2-\\mathbf{D}_1) &= \\sigma \\\\\n",
"\\hat n \\times (\\mathbf{E}_2-\\mathbf{E}_1)&= 0 \\\\\n",
"\\hat n \\cdot (\\mathbf{B}_2-\\mathbf{B}_1) &= 0 \\\\\n",
"\\hat n \\times (\\mathbf{H}_2-\\mathbf{H}_1)&=\\mathbf{K} \\\\\n",
"\\end{aligned}\n",
"$$\n",
"+ $\\hat n$ va de la región 1 a la 2.\n",
"+ $\\sigma$ densidad superficial de carga libre.\n",
"+ $\\mathbf{K}$ corriente superficial de carga libre.\n",
"\n",
"Estas expresiones se pueden escribir en función de otros campos utilizando las relaciones constitutivas\n",
"$$\n",
"\\mathbf{D}(\\mathbf{r}, t)=\\varepsilon_{0} \\mathbf{E}(\\mathbf{r}, t)+\\mathbf{P}(\\mathbf{r}, t), \\quad \\mathbf{B}(\\mathbf{r}, t)=\\mu_{0}[\\mathbf{H}(\\mathbf{r}, t)+\\mathbf{M}(\\mathbf{r}, t)]\n",
"$$\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "GSX28BuvF9Fe"
},
"source": [
"## Ecuaciones de Maxwell para medios i.h.l"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "Lotx0HhPGGWo"
},
"source": [
"Hay medios que, bajo ciertas restricciones, pueden describirse mediante una relacion lineal entre los campos ($\\mathrm{E}$ y $\\mathrm{H}$) y la respuesta del material, el desplazamiento eléctrico $\\mathrm{D}$ y la inducción magnética $\\mathbf{B}$:\n",
"\n",
"$$\n",
"\\mathbf{D}(\\mathbf{r}, t)=\\varepsilon_{0} \\varepsilon \\mathbf{E}(\\mathbf{r}, t), \\quad \\mathbf{B}(\\mathbf{r}, t)=\\mu_{0} \\mu\\mathbf{H}(\\mathbf{r}, t)\n",
"$$\n",
"donde $\\varepsilon$ y $\\mu$ son la permitividad eléctrica y permeabilidad magnéticas relativas.\n",
"\n",
"Si además la corriente libre debida a la conductividad del material se asume de igual forma lineal con el campo eléctrico: $\\mathbf{J}_{\\text {cond }}(\\mathbf{r}, t) =\\sigma \\mathbf{E}(\\mathbf{r}, t)$ y por lo tanto:\n",
"$$\n",
"\\mathbf{J}(\\mathbf{r}, t)=\\mathbf{J}_{0}(\\mathbf{r}, t)+\\sigma \\mathbf{E}(\\mathbf{r}, t) \n",
"$$\n",
"($\\mathbf{J}_{0}$ es la densidad de corriente de las fuentes de campo EM), \n",
"las ecuaciones de Maxwell se pueden escribir como:\n",
"\n",
"$$\n",
"\\begin{aligned}\n",
"\\nabla \\cdot \\mathbf{E}(\\mathbf{r}, t) &=\\rho(\\mathbf{r}, t)/\\varepsilon_{0}\\varepsilon \\\\\n",
"\\nabla \\times \\mathbf{E}(\\mathbf{r}, t) &=-\\mu_{0}\\mu \\frac{\\partial}{\\partial t} \\mathbf{H}(\\mathbf{r}, t) \\\\\n",
"\\nabla \\times \\mathbf{H}(\\mathbf{r}, t) &=\\varepsilon_{0}\\varepsilon\\frac{\\partial}{\\partial t} \\mathbf{E}(\\mathbf{r}, t)+ \\mathbf{J}_{0}(\\mathbf{r}, t)+\\sigma \\mathbf{E}(\\mathbf{r}, t))\\\\\n",
"\\nabla \\cdot \\mathbf{H}(\\mathbf{r}, t) &=0\n",
"\\end{aligned}\n",
"$$\n",
"\n",
"En medios i.h.l no dipersivos y con respuesta local $\\varepsilon,\\mu \\text{ y } \\sigma$ son constantes.\n",
"\n",
"$^{*}$*Estrictamente, solo el vacío.*"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "puZEHKGyKffd"
},
"source": [
"Aproximación lineal\n",
"+ Las ecuaciones de Maxwell definen los campos generados por corrientes y cargas. Sin embargo, no describen como éstas son generadas.\n",
"+ Para resolver de forma auto-consistente las ecuaciones de Maxwell es necesario tener una descripción precisa del comportamiento de la materia bajo la influencia de los campos EM. \n",
"+ Para obtener una descripción completa de la física se da validez a las ecuaciones de Maxwell y se ajustan las relaciones constitutivas (obtenidas experimentalmente o desde la teoría atómica).\n",
"+ Las relaciones constitutivas relacionan las fuentes secundarias, $\\mathbf{P}$ y $\\mathbf{M}$, con los campos EM $\\mathbf{E}$ y $\\mathbf{H}$: $\\mathbf{P}=f[\\mathbf{E}]$ y $\\mathbf{M}=f[\\mathbf{H}]$.\n",
"+ Esto último es equivalente a $\\mathbf{D}=f[\\mathbf{E}]$ y $\\mathbf{B}=f[\\mathbf{H}]$.\n",
"\n",
"Expandiendo $\\mathbf{D}$ en serie de Taylor, vemos que el término de orden menor es lineal con $\\mathbf{E}$\n",
"$$\n",
"D=D_{0}+\\left.\\frac{\\partial D}{\\partial E}\\right|_{D=0} E+\\left.\\frac{1}{2} \\frac{\\partial^{2} D}{\\partial E^{2}}\\right|_{D=0} E^{2}+\\ldots\n",
"$$\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "gIxfR8qEky43"
},
"source": [
""
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "-yqm8qF-Y5Lc"
},
"source": [
"La forma más general de relacionar $\\mathbf{D}$ y $\\mathbf{E}$ se puede escribir como:\n",
"$$\n",
"\\mathbf{D}(\\mathbf{r}, t)=\\varepsilon_{0} \\int_{-\\infty}^{\\infty} \\int_{0}^{\\infty} \\tilde{\\varepsilon}\\left(\\mathbf{r}-\\mathbf{r}^{\\prime}, t-t^{\\prime}\\right) \\mathbf{E}\\left(\\mathbf{r}^{\\prime}, t^{\\prime}\\right) \\mathrm{d}^{3} \\mathbf{r}^{\\prime} \\mathrm{d} t^{\\prime},\n",
"$$\n",
"\n",
"+ La causalidad (no existe respuesta antes de la excitación) fija el intervalo inferior de la integral, $t^{\\prime}=0$. \n",
"+ Un material es dispersivo si la función respuesta,$\\tilde{\\varepsilon}$, depende de $t$. \n",
"+ Un material tiene propiedades no locales si su respuesta en $\\mathbf{r}$ depende de lo que ocurre en otras posiciones. \n",
"\n",
"La expresión anterior es una convolución en espacio y tiempo. Usando las propiedades de la transformada de Fourier en tal caso es posible escribir \n",
"$$\n",
"\\hat{\\mathbf{D}}(\\mathbf{k}, \\omega)=\\varepsilon_{0} \\varepsilon(\\mathbf{k}, \\omega) \\hat{\\mathbf{E}}(\\mathbf{k}, \\omega),\n",
"$$\n",
"donde $\\varepsilon$ es la transformada de Fourier de $\\tilde{\\varepsilon}$. \n",
"\n",
"La mayoría de los materiales no tienen comportamiento no-local, de ahí que:\n",
"$$\n",
"\\hat{\\mathbf{D}}(\\mathbf{r}, \\omega)=\\varepsilon_{0} \\varepsilon(\\omega) \\hat{\\mathbf{E}}(\\mathbf{r}, \\omega),\n",
"$$\n",
"siendo $\\varepsilon(\\omega)$ la constante dieléctrica o permitividad dieléctrica relativa. \n",
"\n",
"Lo mismo ocurre con el campo magnético,\n",
"$$\n",
"\\hat{\\mathbf{B}}(\\mathbf{r}, \\omega)=\\mu_{0} \\mu(\\omega) \\hat{\\mathbf{H}}(\\mathbf{r}, \\omega),\n",
"$$\n",
"donde $\\mu(\\omega)$ es la permeabilidad magnética relativa. \n",
"\n",
"\n",
"Para campos que varían como una función armónica, por ejemplo, $\\hat{\\mathbf{E}}(\\mathbf{r}, \\omega)=e^{-\\imath \\omega t}{\\mathbf{E}}(\\mathbf{r})$, se llega a que.\n",
"$$\n",
"\\mathbf{D}(\\mathbf{r})=\\varepsilon_{0} \\varepsilon(\\omega) \\mathbf{E}(\\mathbf{r}), \\quad \\mathbf{B}(\\mathbf{r})=\\mu_{0} \\mu(\\omega) \\mathbf{H}(\\mathbf{r})\n",
"$$\n",
"\n",
"Finalmente, si $\\varepsilon(\\omega)=\\varepsilon$ y $\\mu(\\omega)=\\mu$ se llega a:\n",
"$$\n",
"\\mathbf{D}(\\mathbf{r})=\\varepsilon_{0} \\varepsilon \\mathbf{E}(\\mathbf{r}), \\quad \\mathbf{B}(\\mathbf{r})=\\mu_{0} \\mu\\mathbf{H}(\\mathbf{r})\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "fqMsaMYUk6_V"
},
"source": [
""
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "-LKUmylXGGFn"
},
"source": [
"## Conservación de la energía. Teorema de Poynting"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "QQcA6QZNGF52"
},
"source": [
"Energía y ecuaciones de Maxwell\n",
"+ Las ecuaciones de Maxwell no contienen información sobre el contenido de energía en el campo. \n",
"+ Para ello se define el teorema de Poynting, una relación \"plausible\" entre el campo EM y su contenido energético.\n",
"\n",
"\n",
"**Teorema de Poynting**\n",
"\n",
"Si se multiplica escalarmente por $\\mathrm{E}$ la ley de Farday y se le resta el producto escalar de $\\mathbf{H}$ por la ley de Ampère se obtiene:\n",
"$$\n",
"\\mathbf{H} \\cdot(\\nabla \\times \\mathbf{E})-\\mathbf{E} \\cdot(\\nabla \\times \\mathbf{H})=-\\mathbf{H} \\cdot \\frac{\\partial \\mathbf{B}}{\\partial t}-\\mathbf{E} \\cdot \\frac{\\partial \\mathbf{D}}{\\partial t}-\\mathbf{J} \\cdot \\mathbf{E} .\n",
"$$\n",
"\n",
"+ La expresión de la izquierda es igual a $\\nabla \\cdot(\\mathbf{E} \\times \\mathbf{H})$. \n",
"+ Se integra ambos lados de la ecuación en todo el espacio. \n",
"+ Se aplica el teorema de Gauss en el lado de la izquierda.\n",
"\n",
"El resultado es:\n",
"$$\n",
"\\oint_{A}(\\mathbf{E} \\times \\mathbf{H}) \\cdot \\mathbf{n} d a=-\\int_{V}\\left[\\mathbf{H} \\cdot \\frac{\\partial \\mathbf{B}}{\\partial t}+\\mathbf{E} \\cdot \\frac{\\partial \\mathbf{D}}{\\partial t}\\right] d V\n",
"-\\int_{V}\\mathbf{J} \\cdot \\mathbf{E} d V\n",
"$$\n",
"\n",
"Pero resulta que:\n",
"$$\n",
"dW/dt = -\\int_{V}\\mathbf{J} \\cdot \\mathbf{E} d V$$ donde\n",
"$dW/dt$ es la rapidez con que se disipa la energía EM por unidad de volumen en forma de calor.\n",
"\n",
"$^{*}$*El trabajo por unidad de tiempo es $d W / d t=\\mathbf{F} \\cdot \\mathbf{v}$. Sustituyendo por la fuerza de Lorentz $d W / d t=q \\mathbf{E} \\cdot \\mathbf{v}+q[\\mathbf{v} \\times \\mathbf{B}] \\cdot \\mathbf{v}$. Ya que $[\\mathbf{v} \\times \\mathbf{B}] \\cdot \\mathbf{v}=[\\mathbf{v} \\times \\mathbf{v}] \\cdot \\mathbf{B}=0$ se obtiene que $\\mathbf{F}=q \\mathbf{v} \\cdot \\mathbf{E}$ que da lugar al término $\\mathbf{J} \\cdot \\mathbf{E}$. Solo el campo eléctrico disipa energía EM.*\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "s6Lc_dqS7Guf"
},
"source": [
"Si asumimos que $\\mathbf{D}=\\varepsilon_{0} \\varepsilon \\mathbf{E}$ y $\\mathbf{B}=\\mu_{0} \\mu \\mathbf{H}$ el primer integrando del primer término de la derecha resulta ser $(1 / 2)\\left[\\varepsilon_{0} \\varepsilon|\\mathbf{E}|^{2}+\\mu_{0} \\mu|\\mathbf{H}|^{2}\\right]$, que es la suma de la densidad de energía electromagnética. \n",
"\n",
"En resumen:\n",
"+ El lado derecho de la ecuación es el ritmo de cambio de la energía EM en $V$.\n",
"+ El lado izquierdo es el flujo de energía hacia fuera o hacia adentro del volumen $V$.\n",
"+ La segunda integral (derecha) representa el ritmo de al que se disipa energía EM dentro de $V$ ($dW/dt$). \n",
"\n",
"El flujo de energía se denota como $\\mathbf{S}$ y se conoce como vector de Poynting.\n",
"$$\n",
"\\mathbf{S}=(\\mathbf{E} \\times \\mathbf{H})\n",
"$$\n",
"\n",
"$^{*}$*El rotacional de cualquier vector podría añadirse a $\\mathrm{S}$ sin cambiar la ley de conservación. Por convenio se elige idéntico a cero.*\n",
"\n"
]
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