Conductors in Electric Field

A point charge $Q$ is placed at the centre of a spherical conducting shell, the shaded part of the figure. A total charge of $-q$ is placed on the shell. The magnitude of the electric field at point $P_1$ at a distance $R_1$ from the centre and the magnitude of the electric field at point $P_2$ a distance $R_2$ from the centre are respectively

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.

A solid conducting sphere of radius $a$ is surrounded by a thin uncharged concentric conducting shell of radius $2a$. A point charge $q$ is placed at a distance $4a$ from common centre of conducting sphere and shell. The inner sphere is then grounded.

Pick up the correct statement.

If a conductor has a potential $V\ne 0$ and there are no charges anywhere else outside, then

A conduction sphere is negatively charged. Which of the following statements is true?

A small sphere is charged to a potential of $50 V$ and a big hollow sphere is charged to potential of $100 V.$ Charge will flow from the smaller sphere to the bigger one when

Infinite conducting ring each having current $i$ in the direction shown are placed concentrically in the plane as shown in the figure. The radius of rings are $r, 2r, 2^{2}r, 2^{3}r\dots \dots \dots \infty$ . The magnetic field at the centre of ring will be

A ball of charge $+50e$ lies at the centre of a hollow spherical metal shell that has a net charge of $-150e$. The charge on the inner surface and outer surface of the spherical shell is:

A spherical conducting ball is suspended by a grounded conducting thread. A positive point charge is moved near the ball. The ball will

A conducting sphere $A$ having a radius $a$ is charged to a potential $V_1$. Now, it is surrounded by another conducting spherical shell of radius $b$. The potential $V_2$ acquired by the sphere $A$ after it is connected to shell $B$ by a thin conducting wire is

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 $Qq > 0$ .)

Assertion: A spark occurs sometimes when an electric iron is switched off.

Reason: The sparking is due to large self-induced emf in the circuit, during make.

Assertion: When a charged body is brought near a neutral conducting body, the induced charge that appears on the nearer surface of the conducting body is always equal and opposite to the charge that has been brought near to it.

Reason: Net electric field inside the conductor is zero. 

The figure shows the charged hollow metal spheres (except $x$) each with an internal radius $a$ and external radius $b$. Match each charge distribution with the corresponding electric field versus radial distance $r$, or the $\left(E-r\right)$ graph.

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A solid conducting sphere of radius $a$ has a net positive charge $2Q$. A conducting spherical shell of inner radius $b$ and outer radius $c$ is concentric with the solid sphere and has a net charge $-\mathrm{Q}$, initially. The surface charge density on the inner and the outer surface of the spherical shell, finally, will be

$\mathrm{A}$ , $\mathrm{B}$ and $\mathrm{C}$ are identical, parallel, conducting plates arranged at equal separations. $\mathrm{B}$ lies between $\mathrm{A}$ and $\mathrm{C}$ . $\mathrm{A}$ and $\mathrm{C}$ are joined together and connected to one terminal of a cell. $\mathrm{B}$ is joined to the other terminal of the cell. $\mathrm{A}$ and $\mathrm{C}$ now have charge $Q$ each. $\mathrm{B}$ has charge $q–$