$A$ current $I$ flows in an infinitely long wire with a cross-section in the form of a semi-circular ring of radius $R$. The magnitude of the magnetic induction along its axis 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 $30 \, \mu T$)

Two long parallel wires are separated by a distance of $2.50 \ cm$. The force per unit length that each wire exerts on the other is $4 \times 10^{-5} \ N \ m^{-1}$, and the wires repel each other. The current in one wire is $0.5 \ A$. What is the current in the second wire (in $A$)? (Take $\mu_0 = 4 \pi \times 10^{-7} \ S.I. \ \text{unit}$)

$A$ 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:

$A$ circular loop and an infinitely long straight conductor carry equal currents,as shown in the figure. The net magnetic field at the centre of the loop is $B_1$,when the current in the loop is clockwise and $B_2$ when the current in the loop is anti-clockwise. Then $\frac{B_1}{B_2}$ is

Find the magnetic field at $P$ due to the arrangement shown.