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 $n$.

 

Given below are two statements.
Statement I : Electric potential is constant within and at the surface of each conductor.

Statement II : Electric field just outside a charged conductor is perpendicular to the surface of the conductor at every point.

In the light of the above statements, choose the most appropriate answer from the options give below.

A hollow conducting sphere is placed in an electric field produced by a point charge placed at $P$ as shown in figure. Let $V_A, V_B, V_C$ be the potentials at points $A, B$ and $C$, respectively. Then

A spherical conductor $A$ is placed concentrically inside a hollow spherical conductor $B$. The charge $+Q$ is given to $A$ and $B$ is earthed. Then the electric field is not zero

Write any five application of superconductors.

Three concentric spherical shells are arranged as shown in the figure. The innermost and outermost spheres are connected to earth. If the middle sphere is given a charge $q_0$. the charges induced in the innermost and outermost spheres respectively are

Consider an initially neutral hollow conducting spherical shell with inner radius $r$ and outer radius $2r.$ A point charge $+Q$ is now placed inside the shell at a distance $\frac{r}{2}$ from the center. The shell is then grounded by connecting the outer surface to the earth. P is an external point at a distance $2r$ from the point charge $+Q$ on the line passing through the center and the point charge $+Q$ as shown in the figure.



The magnitude of the force on a test charge $+q$ placed at P will be

Figure shows three spherical and equipotential surfaces $A, B$ and $C$ round a point charge q. The potential difference${ V}_A-V_B=V_B-V_C$. If $t_1$ and $t_2$ be the distance between them. Then

As shown in figure there are two fixed uniformly charged concentric coplanar conducting rings having radius $R$ and $4R$ and charges $+Q$ and $–8Q$ respectively. A charge particle of mass $m$ & charge $–q$ is projected along the axis of rings from point $P$ so that particle can just reach the center of rings (point $O$ ). (Assume $Qq > 0$ .)

A uniformly charged thin spherical shell of radius $R$ carries uniform surface charge density of $\sigma$ per unit area. It is made of two hemispherical shells, held together by pressing them with force $F$ (see figure). $F$ is proportional to