An $\alpha$-particle and a proton travel with the same velocity in a magnetic field perpendicular to the direction of their velocities. Find the ratio of the radii of their circular paths.

Derive the expression for the magnetic force acting on a moving charge $q$ with velocity $\vec{v}$ in a uniform magnetic field $\vec{B}$.

An electron is projected along the axis of a circular conductor carrying some current. The electron will experience a force:

$A$ charged particle is moving in a uniform magnetic field $(2 \hat{i} + 3 \hat{j}) \text{ T}$. If it has an acceleration of $(\alpha \hat{i} - 4 \hat{j}) \text{ m/s}^2$,then the value of $\alpha$ will be:

In the Thomson experiment for finding $e/m$ for electrons,the beam of electrons is replaced by a beam of muons (particles with the same charge as electrons but with a mass $208$ times that of electrons). The condition for no deflection is satisfied if:

Two infinitely long straight wires $A$ and $B$,each carrying current $I$,are placed on the $x$ and $y$-axes,respectively. The current in wires $A$ and $B$ flows along $-\hat{i}$ and $\hat{j}$ directions,respectively. The force on a charged particle having charge $q$,moving from position $r = d(\hat{i} + \hat{j})$ with velocity $v = v\hat{i}$ is: