Magnetic field $dB$ due to a current element at any point on its axis is . . . . . . .

Magnetic induction is a

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:

$A$ circular coil of wire of radius $r$ has $n$ turns and carries a current $I$. The magnetic induction $B$ at a point on the axis of the coil at a distance $\sqrt{3} r$ from its centre is

Two long wires carrying currents of $8 \,A$ and $6 \,A$ are placed along the $x$-axis and $y$-axis respectively. Find the magnitude of the magnetic field at the point $P(2, 4)$. (Take $\mu_{0} = 4\pi \times 10^{-7} \,T \cdot m/A$)

$A$ thin circular frame of radius $a$ is made of insulating material. $A$ square loop is constructed within it. If the loop carries current $I$,then the magnetic induction at the geometrical centre $O$ will be: