A hollow charged metal sphere has a 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 distance 3r from the centre is -

Question

A hollow charged metal sphere has a 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 distance 3r from the centre is - (A) (V/3 r) (B) (V/4 r) (C) (V/6 r) (D) (V/2 r)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-95euotrjdojc.png" /> VA-VB=(k q/r)-(k q/3 r)=V (k q/r)× (2/3)=V EB=(k q/(3 r)2)=(3/2)(V r/(3 r)2)=(3 V r/2 × 9 × r2)=(V/6 r)

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

$\frac{V}{3 r}$

$\frac{V}{4 r}$

$\frac{V}{6 r}$

$\frac{V}{2 r}$

$V_{A} - V_{B} = \frac{k q}{r} - \frac{k q}{3 r} = V$
$\frac{k q}{r} \times \frac{2}{3} = V$
$E_{B} = \frac{k q}{( 3 r ) ^{2}} = \frac{3}{2} \frac{V r}{( 3 r ) ^{2}} = \frac{3 V r}{2 \times 9 \times r ^{2}} = \frac{V}{6 r}$

Q. A hollow charged metal sphere has a 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 distance 3r from the centre is -

3rV​

4rV​

6rV​

2rV​