||Message]Content page
| Title | Name |
Date  |
|---|---|---|
[NOTES/EM-03005]-Multipole Expansion of PotentialThe large distance expansion of potential due to a localized charge distribution is obtained. The first three terms receiving contributions from the monopole, the dipole moment and the quadrupole moment are explicitly displayed. Important properties of dipole and quadrupole moment are discussed. |
|
24-03-30 05:03:38 |
[LECS/EM-03001]-Electric PotentialThe concept of electric potential for static electric field is defined as work done on a unit charge. The expression for the electric potential of a \(q\) charge is obtained. For a system of point charges the potential can be written down as superposition of potential due to individual charges. As an illustration we compute potential due to a dipole. |
|
24-03-30 05:03:45 |
[LECS/EM-03003]-Electrostatic EnergyThe electrostatic energy of a continuous charge distribution is defined as the energy required to assemble the charges at infinity into the positions as in the given distribution. For a continuous charge distribution it is shown to be \( \dfrac{\epsilon_0}{2}\iiint(\vec E\cdot\vec E) dV\) . Thus a volume of space having nonvanishing electric field has energy density \(\dfrac{\epsilon_0}{2}(\vec E\cdot\vec E)\).The expression for the electrostatic energy reduces to the usual answer \(\frac{1}{2} CV^2\) for a charged parallel plate capacitor. For a uniformly charged sphere of radius \(R\) the electrostatic energy is proved to be equal to \(\frac{3}{5}\Big(\frac{Q^2}{4\pi\epsilon_0 R^2} \Big)\). |
|
24-03-30 05:03:23 |
[LECS/EM-03005] Maxwell's Equations for ElectrostaticsThe Maxwell's equations for electrostatic are derived from Coulomb's law which has been formulated based on experiments. This provides initial experimental evidence for the Maxwell's equations. We discuss two applications of Maxwell's equations. The first result is that the electric field inside an empty cavity in conductors is proved to be zero. The second result is an expression for electric stress tensor is derived. The surface integral of the electric tensor gives the force on charge distribution.
|
|
24-03-30 05:03:52 |
[NOTES/EM-03007]-Work done in field of a point chargeWe discuss the path independence of the work done by static electric field. This leads to, as in mechanics, introduction of the electric potential. An expression of the electric potential is derived by an explicit computation of work done by on a unit positive charge by the electric field of a point charge \(q\). For an arbitrary distribution of charges, the electric potential is obtained by making use of the superposition principle. |
|
24-03-30 05:03:56 |
[NOTES/CM-03005] Charged Particle In Electromagnetic FieldExpression for the Lagrangian for a charged particle in electromagnetic field is given and the Euler Lagrange equations are shown to coincide with EOM with Lorentz force on the charged particle. $\newcommand{\Label}[1]{\label{#1}} \newcommand{\pp}[2][]{\frac{\partial #1}{\partial #2}} |
|
24-03-28 06:03:10 |
[NOTES/CM-03004] Applications of Noether's TheoremExamples of application of Noether's theorem are given for mechanical systems. The following relationship between symmetry and corresponding conservation law is demonstrated by means of explicit examples of system consisting of finite number of particles. $\newcommand{\HighLight}[2][]{\text{[#2]}}$ |
|
24-03-27 10:03:42 |
[NOTES/CM-03002] Symmetries and Conservation LawsSymmetry transformation is defined; statement and the proof of Noether's theorem is given for mechanics of several point particles. $\newcommand{\HighLight}[2][]{}$ |
|
24-03-27 08:03:17 |
[NOTES/CM-03003] Conservation of EnergyThe invariance of the action under time translations leads to conservation of Hamiltonian. This means that the Lagrangian should be independent of time for the law of energy conservation to hold. |
|
24-03-27 04:03:44 |
[NOTES/CM-03006] A short cut to Noether generator and equation for its time variation$\newcommand{\Prime}{^\prime} \newcommand{\pp}[2][]{\frac{\partial #1}{\partial #2}}\newcommand{\dd}[2][]{\frac{d#1}{d#2}}\newcommand{\Lsc}{\mathscr L} $ Gellman-Levi method for computing Noether charge associating with a symmetry transformation is explained, In case of a broken symmetry the Noether generator varies with time and its rate of variation can be computed in a simple manner by the and computing its time variation by this method. |
|
24-03-26 23:03:34 |