Magnetic Field Question

Question

A long wire carrying a current of 100 A is placed in uniform external magnetic field of 5.0 mT. The wire is perpendicular to this magnetic field. Locate the points at which the resultant magnetic field is zero.

Answer 1

For a long wire carrying current I, magnetic field strength at a distance r from center or wire is B = 2 × 10 ^ -7 I / r.  Solve for r, and find the distance from wire at which B = 5.0 mT:

►  r = 2 E-7 I / B = 2 E-7 × 100 / 5 E-3 = 4.00 E-3 m = 4 mm.

The lines of this field follow circular, concentric paths, whose common center is the center of the wire.  Now, magnetic field B is a vector.  The field originated by the 100 A current will add vectorially with the external, constant magnetic field around.  Depending on the relative directions of this external field, and the current-induced field, there will be a line, parallel to the wire, at 4 mm from its center, at which the magnetic field cancels.

Suppose the external, static field is vertical, pointing upwards.  If the current runs left to right, the null-field-line will be located parallel to the wire, on its right side.