$A$ circular current-carrying coil has radius $R$. At what distance from the centre of the coil on the axis,the magnetic induction will become $\frac{1}{8}$ th of its value at the centre of the coil?

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.

$A$ portion of a conductive wire is bent in the form of a semicircle of radius $r$ as shown in the figure. At the centre $O$ of the semicircle,the magnetic induction will be:

$A$ particle carrying a charge equal to $1000$ times the charge on an electron is rotating at $1$ rotation per second in a circular path of radius $r \ m$. If the magnetic field produced at the centre of the path is $x$ times the permeability of vacuum $\mu_0$,the radius $r$ in $m$ is: $[e = 1.6 \times 10^{-19} \ C], [x = 2 \times 10^{-16}]$

What will be the resultant magnetic field at the origin due to four infinite length wires? If each wire produces a magnetic field '$B$' at the origin.

Figures $A$ and $B$ show two long straight wires of circular cross-section (radii $a$ and $b$ with $a < b$),each carrying a current $I$ which is uniformly distributed across the cross-section. The magnitude of the magnetic field $B$ varies with radial distance $r$ from the axis. Which of the following graphs correctly represents the variation of $B$ with $r$ for both wires?