Question

A hollow uniformly charged sphere has radius r. If the potential difference between its surface and a point at a distance 3r from the centre is V then the electric field intensity at a distance 3r form centre is-

• A. V/6r
• B. V/4r
• C. V/3r
• D. V/2r

Answer 1

Answer: (A)

V/6r

Answer 2

V_A =

V_B = $\frac { \mathrm { kq } } { 3 \mathrm { r } }$

V = V_A – V_B = $\frac { \mathrm { kq } } { \mathrm { r } }$ $\left( 1 - \frac { 1 } { 3 } \right)$ = $\frac { 2 \mathrm { kq } } { 3 \mathrm { r } }$

E_B = $\frac { \mathrm { kq } } { ( 3 \mathrm { r } ) ^ { 2 } }$ = $\frac { k ( 3 r ) V } { 9 r ^ { 2 } ( 2 k ) }$ = $\frac { \mathrm { V } } { 6 \mathrm { r } }$