$A$ current carrying circular coil of radius $R$ produces magnetic field $B_1$ at an axial point $P$ at a distance $x$ from its centre and $B_2$ at point $Q$ placed at its centre respectively. If $B_2 = 8B_1$, the value of $x$ is

$A$ long straight wire in the horizontal plane carries a current of $50 \; A$ in the north to south direction. Give the magnitude and direction of $B$ at a point $2.5 \; m$ east of the wire.

$20 \, A$ current is flowing in a long straight wire. The intensity of the magnetic field at a distance of $20 \, cm$ from the wire will be:

$A$ current-carrying wire in its neighbourhood produces:

$A$ symmetric star-shaped conducting wire loop carries a steady current $I$ as shown in the figure. The distance between the diametrically opposite vertices of the star is $4a$. The magnitude of the magnetic field at the center of the loop 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 $\mu_0 = 4\pi \times 10^{-7} \text{ N m A}^{-2}$)