The magnetic force acting on a charged particle of charge $-2\, \mu C$ in a magnetic field of $2\, T$ acting in the $y$-direction,when the particle velocity is $(2\hat{i} + 3\hat{j}) \times 10^6\, m/s$,is:

An electron moving with a speed $u$ along the positive $x$-axis at $y = 0$ enters a region of uniform magnetic field $\overrightarrow B = -B_0 \hat k$ which exists to the right of the $y$-axis. The electron exits from the region after some time with the speed $v$ at coordinate $y$,then

$A$ charged particle is moving in a uniform magnetic field in a circular path. The radius of the circular path is $R$. When the energy of the particle is doubled,the new radius will be:

$A$ tightly wound long solenoid has $n$ turns per unit length,a radius $r$ and carries a current $I$. $A$ particle having charge $q$ and mass $m$ is projected from a point on the axis in a direction perpendicular to the axis. The maximum speed of the particle for which the particle does not strike the solenoid is

Uniform magnetic fields of different strengths ($B_1$ and $B_2$),both normal to the plane of the paper,exist as shown in the figure. $A$ charged particle of mass $m$ and charge $q$,at the interface at an instant,moves into the region $2$ with velocity $v$ and returns to the interface. It continues to move into region $1$ and finally reaches the interface. What is the displacement of the particle during this movement along the interface? (Consider the velocity of the particle to be normal to the magnetic field and $B_2 > B_1$)

An electron is projected with velocity $\vec{v}$ in a uniform magnetic field $\vec{B}$. The angle $\theta$ between $\vec{v}$ and $\vec{B}$ lies between $0^\circ$ and $\frac{\pi}{2}$. Its velocity vector $\vec{v}$ returns to its initial value in a time interval of: