$A$ current $i$ flows in a circular arc of wire of radius $R$,which subtends an angle of $3\pi / 2$ radians at its centre. The magnetic induction at the centre is

Three long straight and parallel wires carrying currents are arranged as shown. The wire $C$ which carries a current of $50 \,A$ is so placed that it experiences no force. The distance of wire $C$ from wire $A$ is (in $\,cm$)

Two concentric circular coils $A$ and $B$ have radii $20 \text{ cm}$ and $10 \text{ cm}$ respectively and lie in the same plane. The current in coil $A$ is $0.5 \text{ A}$ in the anticlockwise direction. What is the current in coil $B$ such that the net magnetic field at the common centre is zero?

$A$ circular coil $A$ has a radius $R$ and the current flowing through it is $I$. Another circular coil $B$ has a radius $2R$ and the current flowing through it is $2I$. The ratio of the magnetic fields at the centre of the circular coils $(B_A : B_B)$ is: (in $:1$)

Two identical coils having the same number of turns and carrying equal current have a common centre,and their planes are at right angles to each other. What is the ratio of the magnitude of the resultant magnetic field at the centre to the magnetic field due to one of the coils at the centre?

An electron moves in a circular orbit with a uniform speed $v$. It produces a magnetic field $B$ at the centre of the circle. The radius of the circle is proportional to