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Removed Charge (Kvpy ’10)

\(12\) positive charges of magnitude \(q\) are placed on a circle of radius \(R\) in a manner that they are …

Maximum Electric Field of a Ring

A ring of radius \(r\) is located in the \(x-y\) plane is given a total charge \(Q=2\pi R\lambda\). Show that …

Electric Field of a Charged Hemisphere

A total charge \(q\) is spread uniformly over the inner surface of a non-conducting hemispherical cup of inner radius \(a\). …

Electric Field from Electric Potential

If the electric potential is given by \(\chi=cxy\), calculate the electric field. Discussion: $$ E_x=-\frac{\partial\chi}{\partial x}=-cy$$ $$ E_y=\frac{\partial \chi}{\partial y}=-cx$$ …

Breakdown Voltage of a Sphere

  What is the maximum charge that can be given to a sphere of diameter \(10cm\) if the breakdown voltage …

Infinite Number of Charges

An infinite number of charges, each equal to \(q\), are placed along the x-axis at \(x=1\),\(x=2\),\(x=4\),\(x=8\) etc. Find the potential …

Tension in a Pendulum inside an Electric Field

A pendulum bob of mass \(80mg\) carries a charge of \(2*10^{-8}C\) at rest in an horizontal uniform electric field of …

Three Charged Spheres

Consider three concentric metallic spheres \(A\), \(B\) and \(C\) of radii of \(a\), \(b\), \(c\) respectively where a<b<c . \(A\) …

Total Charge on a Circular Disc

Consider a circular disc of radius \(a\) whose surface density of charge at any point \((r,\theta\)) is $$ \sigma(r,\theta)=\sigma_0r^2sin^2\theta$$ Find …

Potential of Metal Sphere

A metal sphere having a radius \(r_1\) charged to a potential \(\phi_1\) is enveloped by a thin-walled conducting spherical shell …

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