Electrostatics of Conductors

Two metal spheres of radius $r_1$ and $r_2$, are connected by a thin conducting wire. The second sphere is surrounded by a grounded concentric conducting shell with uniform separation $d$ between their facing surfaces. If the second sphere is given a charge $Q$, find charges acquired by all the three spheres. Assume that $d\ll r_2$, and the distance between the spheres is much larger than their radii.

A conducting sphere of radius $R$ and charge $Q$ is placed near a uniformly charged nonconducting infinitely large thin plate having surface charge density $\sigma$. Then find the potential at point $A$ (on the surface of sphere) due to charge on sphere (here $K=\frac{1}{4\pi {\epsilon }_0}$, ${\theta }_0=\frac{\pi }{3}$) 

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A point charge $q$ is kept inside a conducting shell of radius $2 R$ at a distance of $R$ from center. Magnitude of field due to induced charges on the inner surface of the shell at point $P$ is

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Is the electric field inside a cavity (with no charge) zero, even if the shell is not spherical, but has any irregular shape? Explain.

Charge on both surfaces of middle metal plate

Charges are given to three large parallel conducting plates as shown in figure. Now the switch '$S$' is closed. The value of electric field between the plates (2) and (3) is (each plate has surface of Area A)

A hollow uncharged spherical conductor has inner radius $a$ and outer radius $b$. A positive point charge $+q$ is in the cavity at the centre of the sphere. Find the potential $V\left(r\right)$ everywhere, assuming that $V=0$ at $r\to \infty$,

A spherical conducting shell of inner radius $r_1$ and outer radius $r_2$ has a charge $Q$.

(a) A charge $q$ is placed at the centre of the shell. What is the surface charge density on the inner and outer surfaces of the shell?

(b) Is the electric field inside a cavity (with no charge) zero, even if the shell is not spherical, but has any irregular shape? Explain.

What will be the charges on the sphere after the switch is closed.

There is a conductor with cavity of radius $R$ as shown in figure. A point charge $Q$ is placed at $\frac{R}{2}$ distance from centre of cavity. A point $P$ is at $r$ distance from centre of conductor. If the electric field at point $P$ is $\frac{nQ}{\pi {\epsilon }_0{r}^2},$ then find $n.$

Three identical metallic plates are kept parallel to one another at a separation of $a$ and $b$. The outer plates are connected by a thin conducting wire and a charge $Q$ is placed on the central plate then charge on the inner surface of plate $C$ is

Find the ratio of charges on the inner and outer surfaces of shell $C$, if $Q, 2 Q$ and $-Q$ charges are given to three concentric conducting spherical shells $A, B$ and $C$ respectively as shown in figure.

What is the potential of the metallic shell $B$? If the three concentric metallic shells $A, B$ and $C$, having radii $a, b \text{and} c$ respectively are given surface charge densities $\sigma , -\sigma , \sigma$ respectively. Take $c>b>a$.

A system consists of three concentric metal shells $A$, $B$ and $C$ with radii $a, 2a$ and $3a$ respectively. Shell $B$ is connected to earth and outermost shell is given a charge $Q$. Now if shell $C$ is connected to shell $A$, then the final charge on the shell $B$ is $\frac{-Qx}{11},$ then find the value of $x$.

There are three concentric conducting spherical shells. All of them are charged $Q_1=20 \mathrm{C}$, $Q_2=40 \mathrm{C}, Q_3=60 \mathrm{C}$ and radius $R, 2R, 3R$. The innermost sphere is earthed then find the magnitude of charge transfer from the Earth.

Three concentric metallic spherical shells of radii $R, 2 R, 3 R$ are given charges $Q_1,Q_2,Q_3,$ respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then, the ratio of the charges given to the shells, $Q_1:Q_2:Q_3$, is:-

A charge $Q$ is distributed over two concentric hollow spheres of radii $\left(r\right)$ and $\left(R\right)>\left(r\right)$ such that the surface densities are equal. Find the potential at the common centre.

Can electric field at some point be zero though electric potential is not zero? Give example.

The internal and external pressures for a soap bubble are same. The surface tension of soap solution is $0.04 \mathrm{N}/\mathrm{m}$ and its diameter is $4 \mathrm{cm}$. Determine the charge on soap bubble.

Establish expression for maximum charged density for the equilibrium of a charged soap bubble in a vacuum.