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Constant electric field in vacuum

Node id: 1314page
  • Strength and potential of the field of a point charge $q$:$$ \vec{E}=\frac{1}{4\pi {\varepsilon}_0}\frac{q}{r^3}\vec{r},   \phi=\frac{1}{4\pi {\varepsilon}_0}\frac{q}{r}.$$
  • Relation between field strength and potential:$$\vec{E}=- \vec{\nabla}\phi. $$ i.e. field strength is equal to the anti gradient of the potential.
  • Gauss's theorem and circulation of the vector $\vec{E}$:$$\oint \vec{E}.d\vec{S}=\frac{q}{{\varepsilon}_0}, \oint  \vec{E}.d\vec{r}=0.$$
ranjan's picture 23-10-30 07:10:59 y

Transport Phenomena

Node id: 47page
ranjan's picture 23-10-30 07:10:31 n

Phase Transformations

Node id: 46page
ranjan's picture 23-10-30 07:10:18 n

Liquids. Capillary Effects

Node id: 45page
ranjan's picture 23-10-30 07:10:51 n

The Second Law of Thermodynamics. Entropy

Node id: 44page
ranjan's picture 23-10-30 07:10:28 n

Kinetic Theory of Gases. Boltzmann's Law and Maxwell's Distribution

Node id: 43page
ranjan's picture 23-10-30 07:10:17 n

Equation of the Gas State. Processes

Node id: 41page
ranjan's picture 23-10-30 07:10:37 n

The First Law of Thermodynamics. Heat Capacity

Node id: 42page
ranjan's picture 23-10-30 07:10:27 n

Relativistic Mechanics

Node id: 40page
ranjan's picture 23-10-30 07:10:51 n


Node id: 39page
ranjan's picture 23-10-30 07:10:25 n

Elastic Deformations of a Solid Body

Node id: 38page
ranjan's picture 23-10-30 07:10:54 n

Dynamics of a Solid Body

Node id: 37page
ranjan's picture 23-10-30 07:10:28 n

Universal Gravitation

Node id: 36page
ranjan's picture 23-10-30 07:10:40 n

Laws of Conservation of Energy, Momentum, and Angular Momentum

Node id: 35page
ranjan's picture 23-10-29 07:10:48 n

[LES/EM-07001] Currents and Current Conservation

Node id: 5985collection
kapoor's picture 23-10-29 06:10:20 n

[NOTES/EM-04010] Energy of Charged Capacitor and Force Between the Plates

Node id: 5984page

The electrostatic energy stored in electric field is given by \[\mathcal E = \frac{\epsilon_0}{2}\int |\vec E|^2 d^3r.\] In this article a few selected applications of the above expression for electrostatic energy to the problems involving capacitors are discussed.

kapoor's picture 23-10-27 12:10:10 n

[NOTES/EM-04011] Systems of Several Conductors

Node id: 5983page

Taking examples of a spherical capacitor, we show how the capacitance can be computed using the linearity of relation between the potentials and charges of conductors.

kapoor's picture 23-10-27 11:10:55 n

[NOTES/EM-04014] Electric Potential in Presence of Conductors

Node id: 5982page

The Maxwell's equations imply that the electric potential \(\phi\) obeys Poisson equation \(\nabla^2 \phi = -\rho/\epsilon_0,\) where \(\rho\) is the charged density.

kapoor's picture 23-10-27 10:10:42 n

[NOTES/EM-04013] Example --- The Method of Images

Node id: 5981page

The solution of  a thick shell and a point charge problem by the method of images is outlined.

kapoor's picture 23-10-27 10:10:34 n

The Fundamental Equation of Dynamics

Node id: 34page
ranjan's picture 23-10-26 08:10:00 n