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[YMP/EM-04008] Force Between the Hemispheres Parts of a Uniformly Charged Sphere

Node id: 5929page

A conducting spherical shell of radius \(R\) is placed in a uniform electric field along the \(Z\)- axis.A plane  perpendicular to the electric field divides the shell into two equal halves. Show that  the Coulomb force acting on the hemispherical surfaces which tends to separate them is  across the diametral plane perpendicular to \(\vec E\) is given by
\[ F = \tfrac{9}{4}\pi \epsilon_0 R^2 E_0^2\]

kapoor's picture 23-11-22 12:11:47 n

[YMP/EM-04006] Point Charge and an Infinite Plane

Node id: 5927page


A point charge is placed  at a distance \(d\) from an infinite grounded
conducting plane sheet. Assuming the standard image charge, find

  1. induced surface charge density. Show that the total induced charge is equal to−q
  2. find the potential due to the induced charge;
  3. using Coulomb's law, find the force between the charge and conducting sheet making use of the induced surface charge density on the plane.
kapoor's picture 23-11-22 12:11:19 n

[YMP/EM-04005] Using Maxwell Stress Tensor

Node id: 5926page

Derive  the Coulomb force due to a static charge on another static charge using the Maxwell stress tensor.

kapoor's picture 23-11-22 11:11:30 n

[YMP/EM-04003] Electrostatic energy of a point charge and a grounded infinite conducting plane.

Node id: 5924page

What is the electrostatic energy of a point charge placed near an grounded infinite conducting plane. Show that this is not equal to the energy of the point charge and it image.

kapoor's picture 23-11-22 11:11:19 n

[YMP/EM-04004] Grounded Conducting Sphere in Uniform Electric Field

Node id: 5925page

The problem of a conducting sphere in a uniform electric field is solved. Unlike many other problems, in this problem  the potential does not go to zero as $\longrightarrow \infty$.

kapoor's picture 23-11-21 22:11:49 n

[YMP/EM-04001] Grounded Conducting Sphere and a Point Charge

Node id: 5923page

Two point charges \(Q\) and \(Q^\prime\) are located at positions given by \(\vec{a}, \vec{b},  (a\ne b) \). Find the conditions on \(Q, Q^\prime, a, b \)  so that the potential on the surface of a sphere of radius \(R\) with center at the origin may be zero.

Note the result of this problem is used in solution for electric potential of a grounded conducting sphere in presence of a point charge by the method of images.

kapoor's picture 23-11-20 22:11:46 n

[QUE/EM-ALL] Repository of EM Theory Problems and Questions

Node id: 5841page

This repository is a collection of PROBLEMS and  QUESTIONS in   Electromagnetic Theory.
These are arranged according to topics in the subject.
Not sorted, or arranged, in any particular order within a topic.

Suitable for teachers and content developers only.

Click on any topic to browse all available problems.

(Click opens an embedded  window)

kapoor's picture 23-11-20 20:11:51 n

[NOTES/EM-ALL] Repository of EM Theory NOTES

Node id: 5987page

This is a repository of NOTES in EM-Theory.
Recommended only for authors and content developers.
Not useful for visitors looking for study material.


kapoor's picture 23-11-20 18:11:16 n

[YMP/EM-02005] Field due to a Uniformly Charged Ring

Node id: 6018page

The electric field due to a charged ring, at a point on its axis,  is computed using Coulomb's law.

kapoor's picture 23-11-17 13:11:09 n

[LECS/EM-01001] Units and Constants

Node id: 6008page
kapoor's picture 23-11-16 11:11:17 n

[LECS/EM-01002] Electric and Magentic Fields

Node id: 5857page
kapoor's picture 23-11-10 14:11:34 n

[NOTES/EM-01009] From Action at a Distance to Field Concept

Node id: 5952page

The concept of electric field to describe the interaction of charged particles is briefly explained. Instead of the Coulomb interaction, which is an instantaneous action, we say a charge produces electric field which in turn acts on another charge  present at some other point. Similarly the magnetic force on a current, or a moving charged particle is described in terms of magnetic field produced by a magnet or a current..


AK-47's picture 23-11-10 11:11:46 n

Jumping RIngs

Node id: 6011video_page
kapoor's picture 23-11-10 06:11:59 n

Jumping RIngs

Node id: 6010video_page
kapoor's picture 23-11-10 06:11:54 n

[NOTES/EM-01007] Using dimensional Analysis to get Quick Numerical Estimates

Node id: 5950page

By means of a few examples we show how dimensional analysis can be used to quickly estimate numerical values of expressions occurring in problems.

AK-47's picture 23-11-09 20:11:52 n

[LECS-EM-ALL] Electromagnetic Theory --- NO FRILL LECTURES

Node id: 6009collection
kapoor's picture 23-11-09 08:11:22 n

[LECS/EM-01003] Motion of Charges in Electric and Magnetic Fields

Node id: 6003page

Several examples of motion of  charges in electric and magnetic fields are presented.

kapoor's picture 23-11-07 23:11:14 n

[NOTES/EM-01013] SI System of Units

Node id: 6005page

The Si system of units are explained. This is the system that will be used everywhere in the resources of Proofs program.

kapoor's picture 23-11-07 09:11:39 n

[NOTES/EM-01012] Some Important Constants

Node id: 6004page

The numerical values of a few important constants are listed.

kapoor's picture 23-11-07 07:11:58 n

[NOTES/EM-01014] Gaussian Units

Node id: 6006page

We briefly present Gaussian units and trace  the source of appearance of velocity of light in Maxwell's equations.

kapoor's picture 23-11-07 07:11:44 n