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 $(r << R)$.

$A$ thin rod is bent in the shape of a small circle of radius $r$. If the charge per unit length of the rod is $\sigma$,and if the circle is rotated about its axis at the rate of $n$ rotations per second,the magnetic induction at a point on the axis at a large distance $y$ from the centre is

$A$ long straight wire carries an electric current of $2\,A$. The magnetic induction at a perpendicular distance of $5\,m$ from the wire is

In the previous question,if the current is $i$ and the magnetic field at $D$ has magnitude $B$,

Give two different properties of a current-carrying coil and state Ampere's suggestion.

Two parallel wires in the plane of the paper are at a distance $X_0$ apart. $A$ point charge is moving with speed $u$ between the wires in the same plane at a distance $X_1$ from one of the wires. When the wires carry current of magnitude $I$ in the same direction, the radius of curvature of the path of the point charge is $R_1$. In contrast, if the currents $I$ in the two wires have directions opposite to each other, the radius of curvature of the path is $R_2$. If $\frac{X_0}{X_1}=3$, the value of $\frac{R_1}{R_2}$ is: