A point charge q is surrounded by eight identical charges at distance r as shown in figure. How much work is done by the forces of electrostatic repulsion when the point charge at the centre is removed to infinity?

Question

A point charge q is surrounded by eight identical charges at distance r as shown in figure. How much work is done by the forces of electrostatic repulsion when the point charge at the centre is removed to infinity? (A) Zero (B) (8 q2/4 π ε0 r) (C) (8 q/4 π ε0 r) (D) (64 q2/4 π ε0 r)

Tardigrade Admin · Accepted Answer

W=-q(Vf-Vi)=-q(V∞-Vi)=+q Vi Vi=8 .(k q2/r)=(8 q2/4 π ε0 r) W=(+8 q2/4 π ε0 r)

Q. A point charge $q$ is surrounded by eight identical charges at distance $r$ as shown in figure. How much work is done by the forces of electrostatic repulsion when the point charge at the centre is removed to infinity?

Zero

$\frac{8 q ^{2}}{4 π ε _{0} r}$

$\frac{8 q}{4 π ε _{0} r}$

$\frac{64 q ^{2}}{4 π ε _{0} r}$

$W = - q (V_{f} - V_{i}) = - q (V_{\infty} - V_{i}) = + q V_{i}$
$V_{i} = 8. \frac{k q ^{2}}{r} = \frac{8 q ^{2}}{4 π ε _{0} r}$
$W = \frac{+ 8 q ^{2}}{4 π ε _{0} r}$

Q. A point charge q is surrounded by eight identical charges at distance r as shown in figure. How much work is done by the forces of electrostatic repulsion when the point charge at the centre is removed to infinity?

Zero

4πε0​r8q2​

4πε0​r8q​

4πε0​r64q2​

W=−q(Vf​−Vi​)=−q(V∞​−Vi​)=+qVi​ Vi​=8.rkq2​=4πε0​r8q2​ W=4πε0​r+8q2​

Q. A point charge $q$ is surrounded by eight identical charges at distance $r$ as shown in figure. How much work is done by the forces of electrostatic repulsion when the point charge at the centre is removed to infinity?

$\frac{8 q ^{2}}{4 π ε _{0} r}$

$\frac{8 q}{4 π ε _{0} r}$

$\frac{64 q ^{2}}{4 π ε _{0} r}$

$W = - q (V_{f} - V_{i}) = - q (V_{\infty} - V_{i}) = + q V_{i}$
$V_{i} = 8. \frac{k q ^{2}}{r} = \frac{8 q ^{2}}{4 π ε _{0} r}$
$W = \frac{+ 8 q ^{2}}{4 π ε _{0} r}$