$A$ circular arc of wire of radius of curvature $r$ subtends an angle of $\frac{\pi}{5}$ radian at its centre. If current $i$ is flowing in it, then the magnetic induction at its centre is ($\mu_0$ = permeability of free space).

$A$ long straight wire carrying electric current '$i$' is bent at its point $Q$ to form an angle of $45^{\circ}$ as shown in the figure. The magnetic field at a point $P$ at a distance $d$ from the point $Q$ is:

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 $+\infty$. Find the magnitude of the magnetic field strength at point $(a, 0)$.

The magnetic field induction produced at the centre of orbit due to an electron revolving in $n^{\text{th}}$ orbit of a hydrogen atom is proportional to

Which of the following is a vector quantity?

$A$ 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: $[e = 1.6 \times 10^{-19} \ C], [x = 2 \times 10^{-16}]$