Two concentric coils each of radius equal to $2\pi \text{ cm}$ are placed at right angles to each other. If $3 \text{ A}$ and $4 \text{ A}$ are the currents flowing through the two coils respectively,the magnetic induction (in $\text{Wb m}^{-2}$) at the centre of the coils will be:

What should be the current $i$ (in $A$) in a circular coil of radius $5\,cm$ to annul the horizontal component of Earth's magnetic field ${B_H} = 5 \times {10^{ - 5}}\,T$?

$A$ thin ring of $10 \, cm$ radius carries a uniformly distributed charge. The ring rotates at a constant angular speed of $40 \pi \, rad \, s^{-1}$ about its axis,perpendicular to its plane. If the magnetic field at its centre is $3.8 \times 10^{-9} \, T$,then the charge carried by the ring is close to $\left( \mu_0 = 4 \pi \times 10^{-7} \, N/A^2 \right)$.

$A$ particle carrying a charge equal to $1000$ times the charge on an electron is rotating at $1$ rotation per second in a circular path of radius $r \ m$. If the magnetic field produced at the centre of the path is $x$ times the permeability of vacuum $\mu_0$,the radius $r$ in $m$ is: $[e = 1.6 \times 10^{-19} \ C], [x = 2 \times 10^{-16}]$

Magnetic field intensity $H$ at the centre of a circular loop of radius $r$ carrying current $I$ in e.m.u. is

Two long parallel wires are at a distance $2d$ apart. They carry steady equal currents flowing out of the plane of the paper as shown. The variation of magnetic field $B$ along the line $XX'$ is given by