Question

Charges Q, 2Q and 4Q are uniformly distributed in three dielectric solid spheres 1, 2 and 3 of radii R/2, R and 2R respectively. If magnitudes of the electric fields at point P at a distance R from the centre of spheres 1, 2 and 3 are $E_1,E_2,$ and $E_3$ respectively, then:

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

Answer 1

Answer: (C)

$E_2>E_1>E_3$

For sphere 1:

Using Gauss's law, $E_1.4\pi R^2=\frac{Q}{ϵ}$

$E_1=\frac{kQ}{R^2}$ where $k=\frac{1}{4\pi ϵ}$

For sphere 2:

$E_2.4\pi R^2=\frac{2Q}{ϵ}$

$E_2=2kQ/R^2$

For sphere 3:

Here, $R<2R$, $E_3.4\pi R^2=\frac{\rho .\frac{4}{3}\pi R^3}{ϵ}$ where $4Q=\rho .\frac{4}{3}\pi (2R{)}^3$

$E_3.4\pi R^2=\frac{Q/2}{ϵ}$

$E_3=kQ/2R^2$

Thus, $E_2>E_1>E_3$