A point charge q is surrounded by eight ident | vedclass

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Question

(B) The work done by the electrostatic force when a charge is moved from an initial position to a final position is given by $W = -\Delta U = -(U_f -

Vedclass · Accepted Answer

$\frac{8 q^2}{4 \pi \varepsilon_0 r}$

Vedclass · Answer

(B) The work done by the electrostatic force when a charge is moved from an initial position to a final position is given by $W = -\Delta U = -(U_f - U_i) = U_i - U_f$.Initially,the potential energy $U_i$ of the central charge $q$ due to the eight surrounding charges is the sum of the potential energies of the central charge with each of the eight charges.Since each of the eight charges is at a distance $r$ from the center,the potential at the center due to the eight charges is $V_i = 8 	imes \frac{1}{4 \pi \varepsilon_0} \frac{q}{r} = \frac{8 q}{4 \pi \varepsilon_0 r}$.The initial potential energy of the central charge is $U_i = q V_i = \frac{8 q^2}{4 \pi \varepsilon_0 r}$.When the central charge is moved to infinity,the final potential energy $U_f$ is $0$ because the distance becomes infinite.Therefore,the work done by the electrostatic force is $W = U_i - U_f = \frac{8 q^2}{4 \pi \varepsilon_0 r} - 0 = \frac{8 q^2}{4 \pi \varepsilon_0 r}$.

$A$ point charge $q$ is surrounded by eight identical charges,each of magnitude $q$,at a distance $r$ as shown in the figure. How much work is done by the forces of electrostatic repulsion when the point charge at the center is moved to infinity?

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