|
|
[NOTES/EM-04003] Green Function Method in Electromagnetic TheoryNode id: 5973pageThe Green function method for solution of the Poisson equation with different types of boundary conditions, Dirichlet and Neuman, are discussed.
$\newcommand{\pp}[2][]{\frac{\partial #1}{\partial #2}} \newcommand{\Prime}{^\prime}$ |
|
23-10-25 08:10:04 |
n |
|
|
[NOTES/EM-04002] Poisson Equation in Cylindrical coordinatesNode id: 5972page$\newcommand{\pp}[2][]{\frac{\partial #1}{\partial #2}}$ $\newcommand{\PP}[2][]{\frac{\partial^2#1}{\partial #2^2}}$
Problems with cylindrical symmetry can be solved by separating the variables of the Poisson equation in cylindrical coordinates. The separation of variables for this class of problems and boundary conditions are explained. |
|
23-10-25 06:10:18 |
n |
|
|
[NOTES/EM-04001] Conductors in ElectrostaticsNode id: 5971pageSeveral important properties of perfect conductors in electrostatic situation are discussed. |
|
23-10-25 06:10:04 |
n |
|
|
[NOTES/EM-03021] Intuitive Proof of Path Independence of Work in ElectrostaticsNode id: 5970pageAn intuitive proof of path independence of work done by electrostatic forces is given following Feynman. |
|
23-10-22 21:10:39 |
n |
|
|
[NOTES/EM-03020] Proof of Gauss Law from Maxwell's EquationsNode id: 5969pageA vector calculus proof of Gauss law is given starting from the Maxwell's equation \(\text{div} \vec E=\frac{\rho}{\epsilon_0}\) |
|
23-10-22 21:10:11 |
n |
|
|
[NOTES/EM-03016] Electric Potential of Finite Charged Line SegmentNode id: 5967pageThe electric potential due to charge spread uniformly on a finite line segment is computed.The electric potential due to charge spread uniformly on a finite line segment is computed. |
|
23-10-22 18:10:24 |
n |
|
|
[NOTES/EM-03013] Electrostatic Energy of NucleiNode id: 5966pageThe electromagnetic contribution to the difference in binding energies of mirror nuclei is computed. The numerical values are compared with the binding energy difference
|
|
23-10-22 15:10:26 |
n |
|
|
[NOTES/EM-03015] Energy of a Continuous Charge DistributionNode id: 5965page$\newcommand{\Label}[1]{\label{#1}}\newcommand{\eqRef}[1]{\eqref{#1}}$
The electrostatic energy associated with continuous charge distribution is shown to correspond to energy \(\frac{\epsilon_0}{2} |\vec E|^2\) per unit volume. |
|
23-10-21 06:10:54 |
n |
|
|
[NOTES/EM-03014] Discussion of Electrostatic EnergyNode id: 5964pageThe two expressions for electrostatic energy in terms of the electric field for a systems of point charges and for a continuous charge distributions are discussed. The computation of electrostatic energy for point charges does not include the self energy. This expression can be positive or negative and is zero for a single point charge. On the other hand the expression for energy density for continuous charges is always be positive definite and becomes infinite when applied to a single point charge. |
|
23-10-21 06:10:34 |
n |
|
|
[NOTES/EM-03012] Electrostatic Energy of a CapacitorNode id: 5963pageThe energy stored in a charged capacitor, \(\frac{1}{2}CV^2\) is shown to coincide with the expression derived from the energy density, \(\frac{\epsilon_0}{2}\big(\vec{E}\cdot\vec{E}\big)\), of static fields. |
|
23-10-21 05:10:54 |
n |
|
|
[NOTES/EM-03011]-Summary of Maxwell's equations for ElectrostaticsNode id: 5649pageMaxwell's equations for electrostatics are summarized and relation with the known laws is described. |
|
23-10-19 11:10:51 |
n |
|
|
[NOTES/EM-02014] Flux --- Example of a point chargeNode id: 5961pageThe flux of the electric field of a point charge placed at the centre of a sphere is explicitly computed and shown to be
\[\text{Flux} = \frac{q}{\epsilon_0 }\] |
|
23-10-18 20:10:01 |
n |
|
|
[NOTES/EM-02012] Dipole in Uniform Electric FieldNode id: 5957pageWhen a dipole is placed in a uniform electric field, it experiences a torque given by \(\vec \tau= \vec p \times \vec E\). |
|
23-10-18 19:10:38 |
n |
|
|
[NOTES/EM-02010] Gauss Law and Use of SymmetryNode id: 5956pageGauss law aloe is not sufficient to determine the electric field for a given system.To determine electric field using Gauss law the symmetry of problem plays an important role by determining the direction of the electric field in given problem. |
|
23-10-18 19:10:36 |
n |
|
|
[NOTES/EM-03008]-Maxwell's Second Equations from Coulomb's LawNode id: 5645pageMaxwell's equation, \(\nabla \times \vec{E}=0\), can be easily proved by direct computation of curl of electric field of a point charge and appealing to the superposition principle. |
|
23-10-18 15:10:52 |
n |
|
|
[NOTES/EM-03006]-Electrostatic Energy of a Uniformly Charged Solid SphereNode id: 5643page The electrostatic energy of a uniformly charged solid sphere is computed by computing the energy required to bring infinitesimal quantities and filling up the sphere. |
|
23-10-18 13:10:39 |
n |
|
|
[NOTES/EM-03003]-Maxwell's Equations from Coulomb's Law Node id: 5637pageStarting with the Gauss law and using divergence theorem of vector calculus we derive Maxwell's first equation $\nabla\cdot \vec{E}= \rho/\epsilon_0$. |
|
23-10-18 08:10:34 |
n |
|
|
[NOTES/EM-03002]-Electrostatic EnergyNode id: 5635pageExpressions for electrostatic energy of system of point charges is derived. |
|
23-10-18 08:10:36 |
n |
|
|
[NOTES/EM-03004]-The Electric Stress TensorNode id: 5641pageAn expression for the electric stress tensor is derived for a charge distribution in a volume \(V\). The surface integral of the stress tensor gives the total electric force on the charge in the volume \(V\). |
|
23-10-17 14:10:45 |
n |
|
|
[NOTES/EM-03001]-Computation of Electric PotentialNode id: 5634pageThe curl free nature of the electric field in electrostatics implies existence of a potential,\(\phi(\vec(r))\), from which the electric field can be derived as \(\vec{E}=-\nabla \phi\). The potential at a point is just the work done in moving a unit point charge from infinity to its current position. |
|
23-10-17 14:10:31 |
n |
||Message]