Each of the batteries shown in figure has an emf 5V. Prove that the magnetic field B at the point P is zero for any set of values of the resistances.

A long straight wire carrying current of 25A rests on a table as shown in Fig. 4.3. Another wire PQ of length 1m, mass 2.5 g carries the same current but in the opposite direction. The wire PQ is free to slide up and down. To what height will PQ rise?

Two long wires carrying current I₁ and I₂ are arranged as shown in Fig. 4.1. The one carrying current I₁ is along is the x-axis. The other carrying current I2 is along a line parallel to the y-axis given by x = 0 and z = d. Find the force exerted at O₂ because of the wire along the x-axis.

Two proton beams going in the same direction repel each other whereas tow wires carrying currents in the same direction attract each other. Explain.

(a) Define mutual inductance and write its S.I. unit.

(b) A square loop of side ‘a’ carrying a current I₂ is kept at distance x from an infinitely long straight wire carrying a current I₁ as shown in the figure. Obtain the expression for the resultant force acting on the loop.

Consider the situation described in the previous problem. Suppose the current i enters the loop at the point A and leaves it at the point B. Find the magnetic field at the centre of the loop.

Consider the situation shown in figure. The straight wire is fixed but the loop can move under magnetic force. The loop will

Find the magnetic field B at the centre of a rectangular loop of length ℓ and width b, carrying a current i.

Each of the batteries shown in figure has an emf 5V. Prove that the magnetic field B at the point P is zero for any set of values of the resistances.

The wire ABC shown in figure forms an equilateral triangle. Find the magnetic field B at the centre O of the triangle assuming the wire to be uniform.