An electron moving in a circular orbit of radius $r$ makes $n$ rotations per second. The magnetic field produced at the centre has a magnitude of

$A$ wire in the form of a square of side $a$ carries a current $i$. Then,the magnetic induction at the centre of the square is (Magnetic permeability of free space $= \mu_0$)

Two parallel wires of equal lengths are separated by a distance of $3 \,m$ from each other. The currents flowing through the first and second wires are $3 \,A$ and $4.5 \,A$ respectively in opposite directions. The resultant magnetic field at the mid-point of both the wires is ($\mu_{0} =$ permeability of free space).

Write the equation for the magnetic field due to a circular current-carrying loop at a point on the axis of the loop. Give its special cases.

Two long,straight wires carry equal currents of $10 \ A$ in opposite directions as shown in the figure. The separation between the wires is $5.0 \ cm$. The magnitude of the magnetic field at a point $P$ midway between the wires is . . . . . . $\mu T$. (Given: $\mu_0 = 4\pi \times 10^{-7} \ TmA^{-1}$)

$A$ particle having a charge $50 \ e$ is revolving in a circular path of radius $0.4 \ m$ with $1 \ r.p.s.$ The magnetic field produced at the centre of the circle is $(\mu_0 = 4 \pi \times 10^{-7} \ SI \ units$ and $e = 1.6 \times 10^{-19} \ C)$.