$A$ circular current-carrying coil has a radius $R$. The distance from the centre of the coil on the axis where the magnetic induction will be $\frac{1}{8}$th of its value at the centre of the coil is:

$A$ loop $ABCDA$,carrying current $I=12 \ A$,is placed in a plane,consists of two semi-circular segments of radius $R_1=6 \pi \ m$ and $R_2=4 \pi \ m$. The magnitude of the resultant magnetic field at center $O$ is $k \times 10^{-7} \ T$. The value of $k$ is . . . . . . . (Given $\mu_0=4 \pi \times 10^{-7} \ Tm \ A^{-1}$)

Two infinite wires bent in the form of an $L$ shape carry current $I$ as shown. What is the magnetic field at $O$?

Two circular coils are made from the same wire,but the radius of the $1^{\text{st}}$ coil is twice that of the $2^{\text{nd}}$ coil. If the magnetic field at their centers is the same,then the ratio of the potential difference applied across them is ($1^{\text{st}}$ to $2^{\text{nd}}$ coil).

Connecting wires carrying currents in opposite directions are twisted together in electrical appliances in order to reduce:

The magnetic effect of current was discovered by