$A$ 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:

Two long parallel wires separated by $0.1 \ m$ carry currents of $1 \ A$ and $2 \ A$, respectively, in opposite directions. $A$ third current-carrying wire parallel to both of them is placed in the same plane such that it feels no net magnetic force. It is placed at a distance of

Two long parallel wires carrying currents $I_1 = 4 \ A$ and $I_2 = 3 \ A$ in opposite directions are placed at a distance of $d = 5 \ cm$ from each other. $A$ point $P$ is at equidistance from both the wires such that the lines joining the point $P$ to the wires are perpendicular to each other. The magnitude of the magnetic field at point $P$ is ( $\mu_0 = 4 \pi \times 10^{-7} \ T \cdot m/A$ ).

When an electric current is passed through a solenoid,how can we determine which end behaves as a North pole and which as a South pole? Explain.

$A$ circular coil is in the $y-z$ plane with its centre at the origin. The coil carries a constant current. Assuming the direction of the magnetic field at $x = -25 \, cm$ to be the positive direction of the magnetic field,which of the following graphs shows the variation of the magnetic field along the $x-$ axis?

$A$ thin ring of radius $R$ metre has charge $q$ coulomb uniformly spread on it. The ring rotates about its axis with a constant frequency of $f$ revolution/s. The value of magnetic induction at the centre of the ring in $\text{Wb/m}^2$ is ($\mu_0$ = permeability of free space)