$A$ 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 ......... $J$.

$A$ small sphere of radius $r_{1}$ and charge $q_{1}$ is enclosed by a spherical shell of radius $r_{2}$ and charge $q_{2}$. Show that if $q_{1}$ is positive,charge will necessarily flow from the sphere to the shell (when the two are connected by a wire) no matter what the charge $q_{2}$ on the shell is.

How much kinetic energy will be gained by an $\alpha$-particle in going from a point at $70\,V$ to another point at $50\,V$?

The charge given to a hollow sphere of radius $10\, cm$ is $3.2 \times 10^{-19}\, C$. At a distance of $4\, cm$ from its centre,the electric potential will be

$(a)$ Calculate the potential at a point $P$ due to a charge of $4 \times 10^{-7} \; C$ located $9 \; cm$ away.
$(b)$ Hence,obtain the work done in bringing a charge of $2 \times 10^{-9} \; C$ from infinity to the point $P$. Does the answer depend on the path along which the charge is brought?

$A$ particle $A$ has charge $+q$ and particle $B$ has charge $+4q$,with each of them having the same mass $m$. When allowed to fall from rest through the same electric potential difference $V$,the ratio of their speeds $\frac{v_A}{v_B}$ will be: