Conductors in Electric Field

An isolated system consists of two concentric thin metallic spherical shells $A$ and $B$ having radii $a$ and $2a$ respectively. The shells are neutral initially. A point charge $+q$ is placed at the centre of the shells. The shell $A$ is earthed:

Two concentric conducting spherical shells of radius $r$ and $2r$ are having intial charges$+Q_0$  and $-Q_0$ respectively as shown in the figure. Switch $S$ is closed at time $t=0$. If current through the inductor $L$ at time $\mathrm{t}=\frac{\pi }{4}\sqrt{8\pi \mathrm{L}{\epsilon }_0\mathrm{r}}$ is $\frac{Q_0}{n\sqrt{\pi {\epsilon }_{0}Lr}}$. Find the value of $n$.

There is a system of four conducting parallel plates $A, B, C$ and $D$. Plates $A$ and $C$ are connected to each other with the help of metallic wire and plates $B$ and $D$ are connected to the ground with the help of switches $S_1$ and $S_2$. Distance between consecutive plates is $d$. initially plate $A$ and $B$ are having a charge of $Q_0$ each and plate $D$ is having charge $+2Q_0$ (See figure). At $t=0$ switches $S_1$ and $S_2$ are closed simultaneously. Then choose CORRECT option(s).

A charged spherical conductor has two cavities. A point charge $q_1$ is placed inside the cavity-$1$ and ${\mathrm{q}}_2$ inside the cavity-$2$. '$Q$' charge is given to the conductor. A point charge '$q$' is also placed outside the conductor. Choose the CORRECT alternative(s).

A particle of charge '$\mathrm{q}$' is moved from infinity to the centre of a hollow conducting spherical shell of radius $R$, thickness $t<<R$ through a very tiny hole in the shell. How much work is done by an external agent in the process?

A spherical shell of radius $R$ is given charge $3q$ on its surface and a point charge $q$ is placed at distance $\frac{R}{2}$ from its centre $C$. Also, there is a charge $2q$ placed outside the shell at a distance of $2R$ as shown. Then

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 $x$.

Four concentric thin spherical shells $A, B, C$ and $D$ have radii $a, 2a, 3a$ and $4a$ respectively. Charges $+q$ and $-q$ are given to shells $B$ and $D$ respectively. Shell $C$ is grounded. The potential difference between shell $A$ and $C$ is $V_{\mathrm{A}}-V_{\mathrm{C}}=\frac{kq}{xa}$, where $k=\frac{1}{4\pi {\epsilon }_0}$. What is the value of $x$?

Ground resistance should be designed such that

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.

A very small sphere of mass $80 \mathrm{g}$ having a charge $q$ is held at a height $9 \mathrm{m}$ vertically above the centre of a fixed non conducting sphere of radius $1 \mathrm{m}$, carrying an equal charge $q$. When released it falls until it is repelled just before it comes in contact with the sphere. Calculate the charge $q$.  $\left[g=9.8 \mathrm{m} {\mathrm{s}}^{-2}\right]$

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.

Establish expressions for electric force and electrostatic pressure on the surface of a charged conductor?

You are travelling in a car, lighting is expected, what should you do about your safety?

The excess charge given to a conductor reside always on its outer surface? Why?

A charge $Q$ is a given to a conducting sphere of diameter $d$. What is the value of electric field inside the sphere?