$A$ long straight wire of radius $a$ carries a steady current $i$. The current is uniformly distributed across its cross-section. The ratio of the magnetic field at $a/2$ and $2a$ is

$A$ point charge $Q (= 3 \times 10^{-12} \, C)$ rotates uniformly in a vertical circle of radius $R (= 1 \, mm)$. The axis of the circle is aligned along the magnetic axis of the earth. At what value of the angular speed $\omega$,the effective magnetic field at the centre of the circle will be reduced to zero? (Horizontal component of earth's magnetic field is $30 \, \mu T$)

The magnetic field normal to the plane of a coil of $N$ turns and radius $r$ which carries a current $i$ is measured on the axis of the coil at a distance $h$ from the centre of the coil. This is smaller than the field at the centre by the fraction,

$A$ closely wound circular coil of radius $5\,cm$ produces a magnetic field of $37.68 \times 10^{-4}\,T$ at its center. The current through the coil is $......A$. [Given,number of turns in the coil is $100$ and $\pi=3.14$]

Two parallel conducting wires of equal length are placed distance $d$ apart and carry currents $I_1$ and $I_2$ respectively in opposite directions. The resultant magnetic field at the midpoint of the distance between both the wires is

$A$ circular coil of radius $R$ carries an electric current. The magnetic field due to the coil at a point on the axis of the coil located at a distance $r$ from the centre of the coil,such that $r \gg R$,varies as: