Question

A long, straight wire, which carries a current, is placed in the vicinity of a circular coil. Using the definition of magnetic flux, explain the following statements.

a) When the wire is placed along the diameter of the coil, the net flux through the coil is zero.

b) When the wire is placed along the axis to the coil, the net flux through the coil is zero.

Answer

a) The perpendicular component of the magnetic flux density with respect to the area of the coil on the left side of the coil is into the page.

The perpendicular component of the magnetic flux density with respect to the area of the coil on the right side of the coil is out of the page.

By symmetry, the magnitude of the magnetic flux density on both sides are the same.

Hence, the resultant perpendicular component of the magnetic flux density is zero. Therefore, the magnetic flux through the coil is zero.

b) The magnetic field lines are along the surface of the coil. This means that the perpendicular component of the magnetic flux density with respect to the area of the coil is zero.

Hence, the magnetic flux through the coil is zero.