Two cells of e.m.f. $E_1$ and $E_2$ ($E_1 > E_2$) are connected as shown in figure.

When a potentiometer is connected between points A and B the balancing length of potentiometer wire is $412$ cm. When same potentiometer wire is connected between points A and C the balancing length is $103$ cm. The ratio $E_1 : E_2$ is

The periodic time of a magnet in vibration magnetometer is $T_0$. If a magnet is replaced by another magnet whose moment of inertia is three times and magnetic moment is one-third of the original magnet, then time period of new magnet will be

A square loop ABCD of side L carrying a current $I_1$ is placed at a distance $(L/3)$ from a conductor coplaner with a straight conductor XY carrying current $I_2$ as shown in figure. The net force on the loop will be ($\mu_0$ = magnetic permeability)

A long solenoid carrying a current produces a magnetic field '$B$' along its axis. If the currunt is tripled and the number of turns per cm is halved then new value of magnetic field will be