Two charged spherical conductors of radii R_1 | vedclass

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

Question

(B) The potential $V$ at the surface of a spherical conductor of radius $R$ with charge $Q$ is given by $V = \frac{Q}{4 \pi \varepsilon_0 R}$.Let $Q_1

Vedclass · Accepted Answer

$\frac{R_2}{R_1}$

Vedclass · Answer

(B) The potential $V$ at the surface of a spherical conductor of radius $R$ with charge $Q$ is given by $V = \frac{Q}{4 \pi \varepsilon_0 R}$.Let $Q_1$ and $Q_2$ be the charges on the two spheres with radii $R_1$ and $R_2$ respectively.When the two spheres are connected by a wire,charge flows until their potentials become equal,i.e.,$V_1 = V_2$.Since surface charge density $\sigma = \frac{Q}{4 \pi R^2}$,we have $Q = \sigma \cdot 4 \pi R^2$.Substituting this into the potential formula: $V = \frac{\sigma \cdot 4 \pi R^2}{4 \pi \varepsilon_0 R} = \frac{\sigma R}{\varepsilon_0}$.Equating the potentials: $\frac{\sigma_1 R_1}{\varepsilon_0} = \frac{\sigma_2 R_2}{\varepsilon_0}$.Therefore,the ratio of surface charge densities is $\frac{\sigma_1}{\sigma_2} = \frac{R_2}{R_1}$.

Two charged spherical conductors of radii $R_1$ and $R_2$ are connected by a wire. The ratio of surface charge densities of the spheres $\sigma_1/\sigma_2$ will be

Similar Questions

$A$ charge $+q$ is placed somewhere inside the cavity of a thick conducting spherical shell of inner radius $R_1$ and outer radius $R_2$. $A$ charge $+Q$ is placed at a distance $r > R_2$ from the centre of the shell. Then the electric field in the hollow cavity

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

$A$ 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:

$A$ metal cube is given a positive charge $(+Q)$. Which of the following statements is true?

$A$ solid spherical conducting shell has inner radius $a$ and outer radius $2a$. At the center of the shell, a point charge $+Q$ is located. What must the charge of the shell be in order for the charge density on the inner and outer surfaces of the shell to be exactly equal?

Vedclass Test Series

Exam Paper Generator

Online Exam Module