If two protons are moving with speed $v = 4.5 \times 10^{5} \, m/s$ parallel to each other,then the ratio of electrostatic and magnetic force between them is:

$A$ compass needle free to turn in a horizontal plane is placed at the centre of a circular coil of $30$ turns and radius $12 \;cm$. The coil is in a vertical plane making an angle of $45^{\circ}$ with the magnetic meridian. When the current in the coil is $0.35 \;A$,the needle points west to east.
$(a)$ Determine the horizontal component of the earth's magnetic field at the location.
$(b)$ The current in the coil is reversed,and the coil is rotated about its vertical axis by an angle of $90^{\circ}$ in the anticlockwise sense looking from above. Predict the direction of the needle. Take the magnetic declination at the place to be zero.

Two long current-carrying thin wires,both with current $I$,are held by insulating threads of length $L$ and are in equilibrium as shown in the figure,with threads making an angle $\theta$ with the vertical. If the wires have mass $\lambda$ per unit length,then the value of current $I$ is ($g =$ gravitational acceleration).

If an observer is moving with respect to a stationary electron,then he observes:

$A$ charged particle moves with constant velocity in a region where no effect of gravity is felt, but an electrostatic field $\vec{E}$ together with a magnetic field $\vec{B}$ may be present. Which of the following cases are possible?

The net magnetic field at the centre $O$ of the circle due to the current-carrying loop as shown in the figure is $(\theta < 180^\circ)$.