Question

A solid metal sphere of radius $R$ has a charge $+2Q$. A hollow spherical shell of radius $3R$ placed concentric with the first sphere has net charge - $Q$

• A. The electric field between the spheres at a distance $r$ from the centre of the inner sphere at $R<r<2R$ is $\frac{Q}{2\pi {ϵ}_0{r}^2}$
• B. The potential difference between the spheres is $\frac{Q}{3\pi {ϵ}_{0}R}$
• C. The final distribution of charges if the spheres are joined by a conducting wire is zero on both inner and outer surfaces of the outer sphere
• D. If the inner sphere is earthed, the charge on it is $\frac{Q}{2}$

Answer 1

The correct option is A The electric field between the spheres at a distance $r$ from the centre of the inner sphere at $R<r<2R$ is $\frac{Q}{2\pi {ϵ}_0{r}^2}$

For the outside sphere the electric field becomes. $O$ and for inside sphere it is,

$E=\frac{2Q}{4\Pi {ϵ}_0{r}^2}=\frac{Q}{2\Pi {ϵ}_0{r}^2}$

So, the net electric field becomes $\frac{Q}{2\Pi {ϵ}_0{r}^2}$.