Two charged spherical conductors of radius R_ | vedclass

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

Question

(B) When two conductors are connected by a wire,charge flows until their potentials become equal.Let $V_{1}$ and $V_{2}$ be the potentials of the sphe

Vedclass · Accepted Answer

$\frac{R_{2}}{R_{1}}$

Vedclass · Answer

(B) When two conductors are connected by a wire,charge flows until their potentials become equal.Let $V_{1}$ and $V_{2}$ be the potentials of the spheres. Since they are connected,$V_{1} = V_{2}$.The potential of a charged spherical conductor is given by $V = \frac{kQ}{R}$.Thus,$\frac{kQ_{1}}{R_{1}} = \frac{kQ_{2}}{R_{2}}$,which implies $\frac{Q_{1}}{Q_{2}} = \frac{R_{1}}{R_{2}}$.The surface charge density $\sigma$ is defined as $\sigma = \frac{Q}{A} = \frac{Q}{4\pi R^{2}}$.Therefore,the ratio of surface charge densities is:$\frac{\sigma_{1}}{\sigma_{2}} = \frac{Q_{1} / (4\pi R_{1}^{2})}{Q_{2} / (4\pi R_{2}^{2})} = \frac{Q_{1}}{Q_{2}} 	imes \frac{R_{2}^{2}}{R_{1}^{2}}$.Substituting $\frac{Q_{1}}{Q_{2}} = \frac{R_{1}}{R_{2}}$,we get:$\frac{\sigma_{1}}{\sigma_{2}} = \frac{R_{1}}{R_{2}} 	imes \frac{R_{2}^{2}}{R_{1}^{2}} = \frac{R_{2}}{R_{1}}$.

Two charged spherical conductors of radius $R_{1}$ and $R_{2}$ are connected by a wire. Then the ratio of surface charge densities of the spheres $(\sigma_{1} / \sigma_{2})$ is:

Similar Questions

Conduction electrons are almost uniformly distributed within a conducting plate. When placed in an electrostatic field $\overrightarrow{E}$,the electric field within the plate

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

The figure shows a solid metal sphere of radius $a$ surrounded by a concentric thin metal shell of radius $2a$. Initially, both have charges $Q$ each. When the two are connected by a conducting wire as shown in the figure, the amount of heat produced in this process will be:

Two identical conductors of copper and aluminium are placed in identical electric fields. The magnitude of induced charge in the aluminium will be

$A$ 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:

Vedclass Test Series

Exam Paper Generator

Online Exam Module