A conducting sphere of radius R is charged to a potential of V volt. Then the electric field at a distance r( R) from the centre of the sphere would be

Question

A conducting sphere of radius R is charged to a potential of V volt. Then the electric field at a distance r( > R) from the centre of the sphere would be (A) (R V/r2) (B) (V/r) (C) (r V/R2) (D) (R2 V/r3)

Tardigrade Admin · Accepted Answer

As V=(q/4 π ε0 R) or (q/4 π ε0)=V R dots(i) E=(q/4 π ε0 r2) For r > R ∴ E=(V R/r2) (Using (i))

Q. A conducting sphere of radius $R$ is charged to a potential of $V$ volt. Then the electric field at a distance $r (> R)$ from the centre of the sphere would be

$\frac{R V}{r ^{2}}$

$\frac{V}{r}$

$\frac{r V}{R ^{2}}$

$\frac{R ^{2} V}{r ^{3}}$

As $V = \frac{q}{4 π ε _{0} R}$ or
$\frac{q}{4 π ε _{0}} = V R \dots$ (i)
$E = \frac{q}{4 π ε _{0} r ^{2}}$ For $r > R$
$∴ E = \frac{V R}{r ^{2}}$ (Using (i))

Q. A conducting sphere of radius R is charged to a potential of V volt. Then the electric field at a distance r(>R) from the centre of the sphere would be

r2RV​

rV​

R2rV​

r3R2V​