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[MAP/EM-01001] ----Electric and Magnetic Fields --- The first steps

Node id: 5825path

This map shows evolution of ideas of the electric and magnetic fields for the static charges and steady currents. 

 kapoor's picture 23-01-07 06:01:36 n

[All-Maps/EM Thoery]

Node id: 5828collection

This is a collection of links to maps of key concepts in electromagnetic theory.

 kapoor's picture 23-01-07 06:01:50 n

[MAP/EM-01002] Superposition Principle

Node id: 5826path
 kapoor's picture 23-01-07 05:01:55 n

VDO/EM-01001 Electric Field

Node id: 5824video_page
 kapoor's picture 23-01-04 20:01:59 n

VDO/EM-01001 Electric Field

Node id: 5823video_page
 kapoor's picture 23-01-04 19:01:33 n

All Physics Units ---- Pankaj Sharan

Node id: 5822page 		kapoor's picture 23-01-02 21:01:22 n

Rutherford Scattering

Node id: 5821video_page 		kapoor's picture 22-12-31 05:12:02 n

[QUE/EM-09010] --- EM-PROBLEM

Node id: 3021page
A rod of mass $m$ and length $\ell$ and resistance $R$ starts from rest and slides on two parallel rails of zero resistance as shown in Figure. A uniform magnetic field fill the area A battery and is perpendicular and out of the plane of the paper. A battery of of voltage $V$ is connected as shown in the figure.
Argue that the induced EMF in the loop is $V = Bv\ell $ when the rod has speed  $v$. Write down $F = m\big(\dfrac{dv}{dt}\big)$ and integrate it so show that
\begin{equation*}    v(t) =\frac{V}{B\ell}\Big(1-\exp\Big(- \frac{B^2\ell^2 t}{mR}\Big)\Big).    \end{equation*}

  Rod connected to a battery and sliding on a wire in magnetic field
Hint: Find the limiting speed and separate that out from the total $v$.
kapoor's picture 22-12-08 17:12:28 n

[QUE/EM-05003] --- EM-PROBLEM --- Point charge and a dielectric sphere embedded in another medium

Node id: 2373page

A point charge \(q\) is embedded at the center of a sphere with dielectric  constant \(\kappa_1\). The sphere is itself embedded in an infinite volume with dielectric constant \(\kappa_2\).

  1. Find the electric field inside and outside the sphere;
  2. Obtain the surface charge density of bound charges on the surface of the sphere;
  3. Compute the electric field due to the bound charges outside the sphere;
  4. Verify that the electric field outside, as obtained in part (a) is sum of the fields due to the bound charges and the field of free charge \(q\) embedded in dielectric medium 1.
 kapoor's picture 22-12-08 17:12:09 n

[QUE/EM-05005] --- EM-PROBLEM --- Point charge and two dielectric media separated by a plane boundary

Node id: 2374page

Consider a point charge \(q\)  embedded in a semi-infinite dielectric medium of dielectric ) constant  \(\epsilon_1\), and located a distance  from a plane interface that separates the first medium from another semi-infinite dielectric medium of dielectric constant  \(\epsilon_2\). Suppose that the interface coincides with the plane. Find the electric field everywhere if the distance of the point charge from the interface is \(d\).

 kapoor's picture 22-12-08 16:12:10 n

Wonderful World of WWW

Node id: 3482collection

 

 Links to lot of interesting sites are given. At present it is all unclassified. 

 सकल पदारथ एहि जग माही, कर्महीन नर पावत नाही

 

 kapoor's picture 22-12-07 23:12:56 n

[QUE/EM-04017] EM-PROBLEM

Node id: 2247page

Find the potential between two concentric shell of radii \(a, b > a\) at all points between the shells. It is given that 
\[ V(a) = V_0 \cos\theta,\qquad V(b)=\frac{1}{2} V_0(\cos^2\theta-1)\]

 kapoor's picture 22-12-07 16:12:38 n

[QUE/EM-04011] EM-PROBLEM

Node id: 2383page

The  axis of a charged ring of radius \(a\) makes an angle \(\alpha\) with the \(z\) axis at the origin as shown in the figure. Use separation of variables to find the potential due to the ring at an arbitrary  point. 

 

 kapoor's picture 22-12-07 16:12:37 n

[MCQ/EM-04004] EM-PROBLEM

Node id: 2408page

A charge \( q\) of mass $m$ is kept at a distance \(d\) below a grounded
infinite conducting sheet which lies in the \(xy\) plane. For what value of
\(d\) will the charge remain stationary?

  1.   \( \frac{q}{4\sqrt{mg\pi \epsilon_0}}\)
  2.   \( \frac{q}{\sqrt{mg\pi \epsilon_0}}\)
  3.   There is no finite value of \(d\)
  4.   \(\frac{\sqrt{mg\pi \epsilon_0}}{q}\)

 

CSIR June 2014

 kapoor's picture 22-12-06 18:12:19 n

[MCQ/EM-04003] --- EM-PROBLEM

Node id: 2406page

A point charge \( q\) is placed symmetrically at a distance \( d\) from two perpendicularly grounded conducting infinite plates as shown in the figure. The net force on the charge ( in units of \( 1/(4\pi\epsilon_0)\) is

  1.   \( \dfrac{q^2}{8d^2}(2\surd 2-1) \) away from the corner
  2.   \( \dfrac{q^2}{8d^2}(2\surd 2-1) \) towards from the corner
  3.   \( \dfrac{q^2}{2\surd 2 d^2}\) towards the corner
  4.   \(  \dfrac{q^2}{2\surd 2 d^2}\) away from the corner

 

(CSIR December 2013}  }

 FigBelow{40,10}{60}{60}{em-fig-06003}{}
kapoor's picture 22-12-06 18:12:25 n

[MCQ/EM-04002] EM-PROBLEM

Node id: 2407page

A charged particle is at a distance \( d\) from an infinite conducting plane maintained at zero potential. When released from rest, the particle reaches a speed \( u\) at a distance \( d/2\) from the plane. At what distance from the plane will the particle reach the speed \( 2u\)?

  1.    \( d/6 \)
  2.    \( d/3 \)
  3.    \( d/4 \)
  4.    \( d/5 \)

 

 kapoor's picture 22-12-06 18:12:52 n

[QUE/EM-04006] --- EM-PROBLEM --- Potential of a conducting disk

Node id: 3031page

Show that the potential due to a conducting disk of radius \(a\) and charge \(q\) is \begin{equation}  \phi(r,z) = \frac{q}{4\pi\epsilon_0 a}\int_0^\infty e^{-k|z|} J_0(kr)  \frac{\sin ka }{k}\, dk \end{equation}

 kapoor's picture 22-12-06 18:12:38 n

[QUE/EM-04003] EM-PROBLEM

Node id: 2377page

Two closed equipotentials \(\phi_1\) and \(\phi_2\)are such that \(\phi_1\) contains \(\phi_2\);Let \(\phi\) be the potential at any point \(P\) between them. If a charge \(q\) is now put at point \(P\) and the equipotentials are replaced by grounded conducting surfaces, show that thecharges \(q_1, q_2\),  induced on the two conductors satisfy the relation \[\frac{q_1}{(\phi_2 - \phi_P)} = \frac{q_2}{(\phi_p -\phi_1)} = \frac{q}{(\phi_2 -\phi_1)}\].

Hint

Use Green's reciprocity theorem

 

 kapoor's picture 22-12-06 18:12:38 n

[QUE/EM-04004] EM-PROBLEM

Node id: 2278page

For two concentric spherical shells of radii \(a\) and \(b\)  find the
capacitance matrix
\(Q_1 = C_{11}V_1 + C_{12}V_2; \qquad Q_2= C_{21} V_1+ C_{22} V_2\)

 kapoor's picture 22-12-06 18:12:58 n

[QUE/EM-02021] --- EM-PROBLEM --- Calculating Flux

Node id: 2224page

 


A point charge \(Q\) is placed at a point \(C\)  outside the sphere, and is at a distance \(d > R\) from the centre,

 Two points \(A, B\) are chosen so that the points \(A,B,C\) are in the same plane as the center \(O\) of the sphere and the lines \(OC\) and \(AB\) bisect each other. A plane passing through \(A\) and \(B\) and perpendicular to \(OC\) cuts the spherical surface into two parts   as shown in the figure. a charge \(Q\) is placed at the point \(C\).

 Find  the total  flux of the electric field passing through the two parts of the sphere.
kapoor's picture 22-12-06 17:12:22 n

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