Question

Two spherical conductors $A$ and $B$ of radii $R$ and $2R$ respectively, are separated by a large distance. If some charge is given to both the spheres and later they are connected by a conducting wire, then in equilibrium condition, the ratio of the magnitude of the electric fields at the surface of spheres $A$ and $B$ is

• A. $1:4$
• B. $4:1$
• C. $1:2$
• D. $2:1$

Answer 1

Answer: (D)

When the spherical conductors are connected by a conducting wire, charge is redistributed and the spheres attain a common potential $V$ .
$\therefore$ Intensity ${\text{E}}_{\text{A}}=\frac{1}{4\pi {\epsilon }_0}\frac{{\text{Q}}_{\text{A}}}{{\text{R}}_{\text{A}}^2}$
or or $E_A=\frac{1\times C_{A}V}{4\pi {\epsilon }_0{R}_A^2}=\frac{\left(4\pi {\epsilon }_0{R}_A\right)V}{4\pi {\epsilon }_0{R}_A^2}=\frac{V}{R_A}$
Similarly ${\text{E}}_{\text{B}}=\frac{\text{V}}{{\text{R}}_{\text{B}}}$
$\therefore$ $\frac{{\text{E}}_{\text{A}}}{{\text{E}}_{\text{B}}}=\frac{{\text{R}}_{\text{B}}}{{\text{R}}_{\text{A}}}=\frac{2}{1}$ .