Select the dimensional formula of $\frac{B^2}{2\mu_0}$.

Choose the correct sketch of the magnetic field lines for a pair of parallel current-carrying wires,one with current flowing into the plane (represented by $\otimes$) and one with current flowing out of the plane (represented by $\odot$).

When a proton is released from rest in a room,it starts with an initial acceleration $a_0$ towards west. When it is projected towards north with a speed $v_0$,it moves with an initial acceleration $3a_0$ towards west. The electric and magnetic fields in the room are

Statement $(I)$: $A$ uniform electric field and a uniform magnetic field are pointed in the same direction. If an electron is projected in the same direction,the electron velocity will decrease in magnitude.
Statement $(II)$: Two infinitely long parallel wires are carrying current in the same direction. The magnetic field at a point midway between the wires is zero.
Statement $(III)$: No net force acts on a rectangular coil carrying a steady current when suspended in a uniform magnetic field.
Which of the following is correct?

$A$ long thin-walled pipe of radius $R$ carries a current $I$ along its length. The current density is uniform over the circumference of the pipe. The magnetic field at the center of the pipe due to the quarter portion of the pipe shown is:

The dimensional formula of $\frac{1}{2} \mu_0 H^2$ (where $\mu_0$ is the permeability of free space and $H$ is the magnetic field intensity) is: