A hollow cylindrical wire carries a current $I$ having inner and outer radii $R$ and $2R$, respectively. The magnetic field at a point which is $\frac{3R}{2}$ distance away from its axis is,

Two identical long solenoids $X \text{and} Y$ carry equal current. The magnetic field produced at their axial mid-point is $B$. If both the solenoids are joined to each other according to figure, find magnetic field at axial mid-point of new solenoid.

Three identical long solenoids $P\text{,} Q \text{and} R$ are connected to each other as shown in figure. If the magnetic field at the centre of $P$ is $2.0 \mathrm{T}$, what would be the field at the centre of $Q$?

A charge ${10}^{–11} \mathrm{Cb}$ and $10^{–7} \mathrm{kg}$ mass moves with a velocity of ${10}^8 \mathrm{m} {\sec }^{-1}$ along $x$-axis. A uniform static magnetic field $0.5 \mathrm{T}$ is acting along the $y-$axis. The magnetic force (magnitude and direction) on charge is,