$A$ charge of $8 \; mC$ is located at the origin. Calculate the work done in $J$ in taking a small charge of $-2 \times 10^{-9} \; C$ from a point $P (0, 0, 3 \; cm)$ to a point $Q (0, 4 \; cm, 0)$,via a point $R (0, 6 \; cm, 9 \; cm)$.

$64$ identical drops each charged up to a potential of $10 \, mV$ are combined to form a bigger drop. The potential of the bigger drop will be $.......... \, mV$.

The electric potential at the surface of an atomic nucleus $(Z=50)$ of radius $9 \times 10^{-15} \ m$ is . . . . . . .

$A$ uniformly charged solid sphere of radius $R$ has potential $V_0$ (measured with respect to $\infty$) on its surface. For this sphere, the equipotential surfaces with potentials $\frac{3V_0}{2}, \frac{5V_0}{4}, \frac{3V_0}{4}$, and $\frac{V_0}{4}$ have radii $R_1, R_2, R_3$, and $R_4$ respectively. Then:

$A$ proton has a mass $1.67 \times 10^{-27} \,kg$ and charge $+1.6 \times 10^{-19} \,C$. If the proton is accelerated through a potential difference of $1$ million volts,then the kinetic energy is ......... $J$.

$A$ proton is accelerated through $50,000 \, V$. Its energy will increase by