An electron makes a full rotation in a circle of radius $0.8 \ m$ in one second. The magnetic field at the centre of the circle is $(\mu_0 = 4 \pi \times 10^{-7} \text{ SI units})$.

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 $\mu_{0} = 4\pi \times 10^{-7} \,T \cdot m/A$)

$A$ small cube of side $1 \ mm$ is placed at the center of a circular loop of radius $20 \ cm$. If the current in the loop is $2 \ A$,then the magnetic energy stored inside the cube is (Assume $\mu_0 = 4 \pi \times 10^{-7} \ SI$ units).

Which scientist established that electricity and magnetism are interrelated?

$A$ current of $1 \, A$ flows through an infinitely long straight wire. The magnetic field produced at a point $1 \, m$ away from it is:

Two infinitely long wires each carrying the same current $i$ and pointing in $+y$ direction are placed in the $xy$ plane,at $x=-2 \ cm$ and $x=1 \ cm$. An electron is fired with speed $U$ from the origin making an angle of $+45^{\circ}$ from the $x$-axis. The force on the electron at the instant it is fired is [$B_0$ is the magnitude of the field at the origin due to the wire at $x=1 \ cm$ alone].