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The electric field at a distance $\frac{3R}{2}$ from the centre of a charged conducting spherical shell of radius R is E. The electric field at a distance $\frac{R}{2}$ from the centre of the sphere is
A
Zero
B
E
C
$\frac{E}{2}$
D
$\frac{E}{3}$
Detailed Solution
The point at $\frac{R}{2}$ lies inside the conducting shell.
Take a spherical Gaussian surface of radius $\frac{R}{2}$ concentric with the shell. All the charge of a conductor resides on its outer surface, so the charge enclosed is zero.
By Gauss's law, $E\times4\pi r^2 = \frac{q_{enclosed}}{\varepsilon_0} = 0$
So the field at every point inside the shell is zero, whatever the field E outside (at $\frac{3R}{2}$) may be.
Electric field at $\frac{R}{2}$ = zero
Take a spherical Gaussian surface of radius $\frac{R}{2}$ concentric with the shell. All the charge of a conductor resides on its outer surface, so the charge enclosed is zero.
By Gauss's law, $E\times4\pi r^2 = \frac{q_{enclosed}}{\varepsilon_0} = 0$
So the field at every point inside the shell is zero, whatever the field E outside (at $\frac{3R}{2}$) may be.
Electric field at $\frac{R}{2}$ = zero