Question

The charges $Q,2Q\text{and}4Q$ are uniformly distributed in three dielectric solid spheres of radii $R/2,R\text{and}2R$ respectively as shown in the figure. If the magnitudes of electric field at the point $P$ at a distance $R$ from the centre of the spheres $\text{I, II}$ and $\text{III}$ are $E_1,E_2\text{and}{E}_3$ respectively, then

• A. $E_1>E_2>E_3$
• B. $E_3>E_2>E_1$
• C. $E_2>E_1>E_3$
• D. $E_3>E_1>E_2$

Answer 1

The correct option is C $E_2>E_1>E_3$

The electric field at a point outside the dielectric sphere is $E=\frac{Q}{4\pi {ϵ}_0{r}^2}$
and that at a point inside is $E=E_{\text{surface}}\times \frac{r}{R}$, where $r$ is the distance from the centre.
$E_1=\frac{1}{4\pi {ϵ}_0}\frac{Q}{R^2}$
$E_2=\frac{1}{4\pi {ϵ}_0}\frac{2Q}{R^2}$ and
$E_3=\frac{1}{4\pi {ϵ}_0}\frac{4Q}{4R^2}$
$\therefore E_1:E_2:E_3=2:4:1$
Thus, $E_2>E_1>E_3$
Hence, option $\left(C\right)$ is correct.