$A$ particle of charge $Q$ and mass $m$ travels through a potential difference $V$ from rest. The final momentum of the particle is

An arc of radius $r$ carries a charge. The linear charge density is $\lambda$ and the arc subtends an angle of $\frac{\pi}{3}$ at the centre. What is the electric potential at the centre?

$A$ positively charged ring is in the $y-z$ plane with its centre at the origin. $A$ positive test charge $q_0$,held at the origin,is released along the $x$-axis. Then its speed

Two conducting hollow spheres of radii $R$ and $3R$ are found to have $Q$ charge on their outer surfaces when both are connected with a long wire. $A$ charge $q'$ is kept at the centre of the bigger sphere. Which of the following is true?

Derive an expression for the electric potential at a distance $r$ from a positive point charge $Q$.

An electric dipole is placed as shown in the figure. The electric potential (in $10^2 \ V$) at point $P$ due to the dipole is ($\epsilon_0 =$ permittivity of free space and $\frac{1}{4 \pi \epsilon_0} = K$):