Two isolated metallic solid spheres of radii | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Initial charges on the spheres are:$Q_1 = \sigma(4\pi R^2) = 4\pi R^2\sigma$$Q_2 = \sigma(4\pi(2R)^2) = 16\pi R^2\sigma$Total charge $Q = Q_1 + Q_

Vedclass · Accepted Answer

$\frac{5}{6}$

Vedclass · Answer

(D) Initial charges on the spheres are:$Q_1 = \sigma(4\pi R^2) = 4\pi R^2\sigma$$Q_2 = \sigma(4\pi(2R)^2) = 16\pi R^2\sigma$Total charge $Q = Q_1 + Q_2 = 20\pi R^2\sigma$.When connected by a wire,the potentials become equal:$V_1 = V_2 \implies \frac{kQ_1^{\prime}}{R} = \frac{kQ_2^{\prime}}{2R} \implies Q_2^{\prime} = 2Q_1^{\prime}$.Since charge is conserved,$Q_1^{\prime} + Q_2^{\prime} = 20\pi R^2\sigma$.Substituting $Q_1^{\prime} = \frac{Q_2^{\prime}}{2}$,we get $\frac{Q_2^{\prime}}{2} + Q_2^{\prime} = 20\pi R^2\sigma \implies \frac{3}{2}Q_2^{\prime} = 20\pi R^2\sigma \implies Q_2^{\prime} = \frac{40}{3}\pi R^2\sigma$.The new charge density of the bigger sphere is $\sigma^{\prime} = \frac{Q_2^{\prime}}{4\pi(2R)^2} = \frac{Q_2^{\prime}}{16\pi R^2}$.Substituting $Q_2^{\prime}$,we get $\sigma^{\prime} = \frac{40\pi R^2\sigma}{3 \cdot 16\pi R^2} = \frac{40\sigma}{48} = \frac{5}{6}\sigma$.Therefore,$\frac{\sigma^{\prime}}{\sigma} = \frac{5}{6}$.

Similar Questions

$A$ conducting sphere of radius $10\, cm$ is charged with $10\,\mu C$. Another uncharged sphere of radius $20\, cm$ is allowed to touch it for some time. After the spheres are separated,the ratio of the surface charge densities on the spheres will be:

Consider the shown system of two concentric thin metal shells. The inner shell has charge $Q$,while the outer shell is neutral. The potential difference between the shells is $V$. If the shells are joined by a metal wire,then the potential of the inner shell is

$A$ thin metallic spherical shell contains a charge $Q$ on it. $A$ point charge $+q$ is placed at the centre of the shell and another charge $q'$ is placed outside it as shown in the figure. All the three charges are positive. The force on the central charge due to the shell is:

The metal plate on the left in the figure carries a charge of $+q$. The metal plate on the right has a charge of $-2q$. What charge will flow through the switch $S$ when it is closed,if the central plate is initially neutral?

The figure shows three concentric metallic spherical shells. The outermost shell has charge $q_2$,the innermost shell has charge $q_1$,and the middle shell is uncharged. The charge appearing on the inner surface of the outermost shell is

Vedclass Test Series

Exam Paper Generator

Online Exam Module