Question

A spherical capacitor has an inner sphere of radius $12cm$ and an outer sphere of radius $13cm$. The outer sphere is earthed, and the inner sphere is given a charge of $2.5\mu C$. The space between the concentric spheres is filled with a liquid of dielectric constant $32$. Determine the potential of the inner sphere :

• A. $500V$
• B. $450V$
• C. $400V$
• D. $300V$

Answer 1

Answer: (B)

As outer sphere is earthed so its potential is zero. Let the potential of inner sphere is $V$.

Using Gauss's law the field at a distance $r$ from the center in between the sphere is:

$E.4\pi r^2=\frac{Q}{ϵ}\Rightarrow E=\frac{Q}{4\pi k{ϵ}_0{r}^2}$ as dielectric constant, $(k=\frac{ϵ}{{ϵ}_0})$