Question

The electric field at 20 cm from the centre of a uniform charge non - conducting sphere of radius 10 cm is E . Then at a distant 5 cm from the centre it will be

• A. 16 E
• B. 4 E
• C. 2 E
• D. Zero

Answer 1

The correct option is C 2 E

For a non-conducting sphere containing a distributed charge Q and of radius R, the electric field in given by at a distance 'r'

$E=\{\begin{array}{cc}\frac{KQ}{r^2},& whenr>R\left(outside\right)fromcentre\\ \frac{pr}{3t_0},& whenr<R\left(inside\right)kwherep=\frac{Q}{V}\left[chargedensity\right]\end{array}$

at a distance $r=20cm$, field is $E(r>R)$ where $R=10cm$ (Radius of sphere)

So, $E=\frac{KQ}{2O^2}\Rightarrow Q=\frac{400E}{K}=1600\pi {\in }_{0}E$ (as $K=\frac{1}{4\pi {\in }_0}$)

now volume of sphere, $V=\frac{4}{3}\pi R^3$

so at a distance $r=5cm,(r<R)$, inside sphere :-

$E^{\prime }=\frac{pr}{3t_0}=\frac{Qr}{v3t_0}$

$=\frac{1600\pi {\in }_{0}E\times 5}{\frac{4}{3}\pi \times L{O}^3\times 3\times t_0}=\frac{2000E}{1000}=2E$

$\therefore E^{\prime }=2E$