Two concentric and coplanar rings of radius $r$ and $R$ are shown in the figure. Find the magnetic flux linked through the smaller coil when the same current $I$ flows through each in opposite directions $(r << R)$.

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 $cm$)

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?

$A$ wire has three different sections as shown in the figure. The magnitude of the magnetic field produced at the centre '$O$' of the semicircle by the three sections together is $(\mu_0 = \text{permeability of free space})$:

At what distance on the axis,from the centre of a circular current-carrying coil of radius $r$,does the magnetic field become $1/8$th of the magnetic field at the centre?

$A$ small current element of length $d\ell$ carrying current $I$ is placed at $(1, 1, 0)$ and is carrying current in the $+z$ direction. If the magnetic field at the origin is $\vec{B}_1$ and at the point $(2, 2, 0)$ is $\vec{B}_2$,then: