Question

Chapter 29, Problem 009 Two long straight wires are parallel and 8.6 cm apart. They are to carry equal currents such that the magnetic field at a point halfway between them has a magnitude 350 µT. (a) Should the currents be in the same or opposite directions? (b) How much current is needed?

Answer 1

Given the distance between the parallel wires d = 8.6cm. So the distance from the centre to each of the wire is r = 4.3cm. The magnitude of the magnetic field is B = 350T.

(a) The direction of the magnetic field at the centre is given by Right Hand Thumb Rule. If the current flowing through the wires are in the same direction and since the currents through each wires have equal magnitude, the net field will be zero.

If the current is flowing in the opposite direction, net field at the centre will not be zero. So the current is flowing in the opposite direction.

(b) Since the current is flowing in the opposite direction, the net magnetic field at the centre by both the wires is given by,

But given,

Therefore,

So the current needed in each wire is 37.6A.