Question

Some positive charge is spread uniformly over the surface of a thin spherical shell. Radius of sphere is $100cm$ and electric field on the surface is $90\times {10}^{3}N/C$. A point $A$ is at $50cm$ from the centre & point $B$ is at $150cm$ from the centre. Field at $A$ & $B$ are $E_A$ & $E_B$ respectively, then

• A. $E_A=E_B=45\times {10}^{3}N/C$
• B. $E_A=0,E_B=45\times {10}^{3}N/C$
• C. $E_A=0,E_B=40\times {10}^{3}N/C$
• D. $E_A=E_B=40\times {10}^{3}N/C$

Answer 1

The correct option is C $E_A=0,E_B=40\times {10}^{3}N/C$

The point $A$ lies inside the shell,
$E_A=E_{inside}=0$
The point $B$ is outside the sphere,
$E_B=\frac{kq}{r^2}=\frac{kq}{(3R/2{)}^2}$
$=\frac{4}{9}\left(\frac{kq}{R^2}\right)$
$=\frac{4}{9}\times E_{surface}$
$=\frac{4}{9}\times 90\times {10}^3$
$=40\times {10}^{3}N/C$