Question

You are moving a negative charge $q<0$ at a small constant speed away from a uniformly charged non-conducting spherical shell on which resides a negative charge $Q<0$. The electrostatic field of $Q$ is $E$. Let $U$ be the total energy of the system, $W_a$ the work done by the force $F_a$ you exert on $q$ and $W_E$ the work done by the electrostatic force $F_E$ on $q$. Then, as $q$ is being moved,

• A. $W_a=W_E$, therefore $U$ remains constant
• B. $F_a=-F_E$
• C. $U$ increases
• D. $U$ decreases

Answer 1

Answer: (B), (D)

The correct options are
B $F_a=-F_E$
D $U$ decreases

If charge is being moved slowly, ${\overrightarrow{F}}_a=-{\overrightarrow{F}}_E$
$Wa+W_E=\Delta KE=0$ [charge is moved slowly]
i.e. $W_a=-W_E$
As force $F_a$ and displacement are ${180}^{\circ }$,
$\overrightarrow{F}.\overrightarrow{dr}<0$
$W_a<0$
Here total energy of system is equal to elecrostatic potential energy
$U=\frac{KQq}{r}$
As $r$ increases, $\Delta U<0$
Therefore, $U$ decreases.