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).

The dimension of the magnetic field intensity $B$ is

$A$ circular arc of radius $r$ carrying current $I$ subtends an angle $\frac{\pi}{8}$ at its centre. The radius of the metal wire is uniform. The magnetic induction at the centre of the circular arc is ($\mu_0 =$ permeability of free space).

Two long straight parallel conductors carry currents $I_1$ and $I_2$ $(I_1 > I_2)$. When the direction of $I_1$ and $I_2$ is the same,the magnetic field intensity midway between the two conductors is $20 \mu T$. If the direction of $I_2$ is reversed,the field intensity becomes $50 \mu T$. The ratio $I_2 / I_1$ is:

$A$ wire in the form of a circular loop of one turn carrying a current produces a magnetic field $B$ at the centre. If the same wire is looped into a coil of two turns and carries the same current,the new value of magnetic induction at the centre is

Magnetic induction is a