In the diagram,$I_{1}$ and $I_{2}$ are the strengths of the currents in the loop and straight conductor,respectively. Given $OA = AB = R$. The net magnetic field at the centre $O$ is zero. Then the ratio of the currents in the loop and the straight conductor is:

$A$ current-carrying circular loop of radius '$R$' and a current-carrying long straight wire are placed in the same plane. The currents through the circular loop and the long straight wire are '$I_C$' and '$I_w$' respectively. The perpendicular distance between the centre of the circular loop and the wire is '$d$'. The magnetic field at the centre of the loop will be zero when the separation '$d$' is equal to:

$A$ circular loop is kept in the vertical plane that contains the north-south direction. It carries a current that is towards the south at the topmost point. Let $A$ be a point on the axis of the circle to the east of it and $B$ be a point on this axis to the west of it. The magnetic field due to the loop is:

State and explain the Biot-Savart law for the magnetic field produced by a current element. Give the direction of the magnetic field and define its unit.

An infinitely long wire carrying current $I$ is along the $Y$-axis such that its one end is at point $A(0, b)$ while the wire extends up to $+\infty$. The magnitude of the magnetic field strength at point $(a, 0)$ is:

The unit of magnetic induction is