$A$ 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).

Two concentric circular coils of ten turns each are situated in the same plane. Their radii are $20 \ cm$ and $40 \ cm$ and they carry respectively $0.2 \ A$ and $0.3 \ A$ current in opposite directions. The magnetic field in $Wb/m^2$ at the centre is:

Find the magnitude of the magnetic field at point $p$ due to the semi-infinite wire shown below.

The fractional change in the magnetic field intensity at a distance $r$ from the centre on the axis of a current-carrying coil of radius $a$ to the magnetic field intensity at the centre of the same coil is: (Take $r << a$)

In the figure,find out the magnetic field at the center $B$ (Given $I = 2.5 \; A, r = 5 \; cm$).

$A$ straight wire carrying a current of $12\; A$ is bent into a semi-circular arc of radius $2.0\; cm$ as shown in Figure $(a)$. Consider the magnetic field $B$ at the centre of the arc.
$(a)$ What is the magnetic field due to the straight segments?
$(b)$ In what way does the contribution to $B$ from the semicircle differ from that of a circular loop and in what way does it resemble?
$(c)$ Would your answer be different if the wire were bent into a semi-circular arc of the same radius but in the opposite way as shown in Figure $(b)$?