When a helium nucleus covers a circle of radius $0.8 \,m$ in $2 \,s$, find the value of magnetic field $B$ at the centre of the circle.

$A$ horizontal overhead powerline is at a height of $5 \,m$ from the ground and carries a current of $150 \,A$ from East to West. The magnetic field directly below it on the ground is

Two mutually perpendicular conductors carrying currents $I_1$ and $I_2$ lie in one plane. The locus of the point at which the magnetic induction is zero,is a

In the figure,two parallel infinitely long current-carrying wires are shown. If the resultant magnetic field at point $A$ is zero,then determine the current $I$ (in $A$).

$A$ circular coil of wire of radius $r$ has $n$ turns and carries a current $I$. The magnetic induction $B$ at a point on the axis of the coil at a distance $\sqrt{3} r$ from its centre is

$A$ rod with a circular cross-section area $2 \text{ cm}^2$ and length $40 \text{ cm}$ is wound uniformly with $400$ turns of an insulated wire. If a current $0.4 \text{ A}$ flows in the wire winding, the total magnetic flux produced inside the winding is $4\pi \times 10^{-6} \text{ Wb}$. The relative permeability of the rod is (Given permeability of vacuum $\mu_0 = 4\pi \times 10^{-7} \text{ N m A}^{-2}$)