A proton and a deuteron having equal momenta enter in a region of uniform magnetic field at right angle to the direction of the field. Depict their trajectories in the field.

An $\alpha$-particle and a proton moving with the same speed enter the same magnetic field region at right angles to the direction of the field, as shown in Figure (a). Show the trajectories followed by the two particles in the region of the magnetic field. Find the ratio of the radii of the circular paths which the two particles may describe.

As shown in Figure, a rectangular loop of width $l$ is suspended from the insulated hook of a spring balance. A current $I$ flows in the anticlockwise direction in the loop. A magnetic field $B$ exists in the lower region. What will be the change in the tension of the spring if the current in the loop is reversed ?

A loosely wound helix made of stiff wire is mounted vertically with its lower end just touching a dish of mercury, as shown in Figure. When a current from a battery is started in the coil through the mercury, the wire executes oscillatory motion with the lower end jumping out of and into the mercury. Give reason.

A horizontal wire $AB$ of length $\text{'}I\text{'}$ and mass $\text{'}m\text{'}$ carries a steady current $I_1$, free to move in vertical plane is in equilibrium at a height of $\text{'}h\text{'}$ over another parallel long wire $CD$ carrying a steady current $I_2$, which is fixed in a horizontal plane as shown. Derive the expression for the force acting per unit length on the wire $AB$ and write the condition for which wire $AB$ is in equilibrium.

Figure shows three infinitely long straight parallel current carrying conductors. Find the
(i) magnitude and direction of the net magnetic field at point $A$ lying on conductor $1$.

Figure shows three infinitely long straight parallel current carrying conductors. Find the (ii) magnetic force on conductor $2$.