$A$ coil having $N$ turns carries a current $I$ as shown in the figure. The magnetic field intensity at point $P$ is

Two points $A$ and $B$ on the axis of a circular current loop are at distances of $4 \ cm$ and $3 \sqrt{3} \ cm$ from the centre of the loop. If the ratio of the induced magnetic fields at points $A$ and $B$ is $216: 125$, the radius of the loop is (in $cm$)

An arc of a circle of radius $R$ subtends an angle $\frac{\pi}{2}$ at the centre. It carries a current $i$. The magnetic field at the centre will be

An electric current $I$ enters and leaves a uniform circular wire of radius $r$ through diametrically opposite points. $A$ particle carrying a charge $q$ moves along the axis of the circular wire with speed $v$. What is the magnetic force experienced by the particle when it passes through the centre of the circle?

Consider two thin identical conducting wires covered with very thin insulating material. One of the wires is bent into a loop and produces a magnetic field $B_1$ at its centre when a current $I$ passes through it. The second wire is bent into a coil with three identical loops adjacent to each other and produces a magnetic field $B_2$ at the centre of the loops when a current $I/3$ passes through it. The ratio $B_1 : B_2$ is

An infinite wire has a circular bend of radius $a$, and carries a current $I$ as shown in the figure. The magnitude of the magnetic field at the origin $O$ is given by: