Question

If magnetic monopoles existed, the right-hand side of Eq. (29.20) would include a term proportional to the current of magnetic monopoles. Suppose a steady monopole current is moving in a long straight wire. Sketch the electric field lines that such a current would produce.

Short answer

An electric field is generated around a monopole current in the same way that a magnetic field is generated around a current-carrying conductor.

However, the direction of the electric field would be opposite to the magnetic field created by an electric current.

Step-by-step solution

Step 1:

Maxwell's equation for a magnetic monopole is:

Here $q_m$denotes the magnetic charge, and $I_m$is the monopole current generated only to meet the magnetic monopole assumption. These equations are derived from the symmetry of Maxwell's equations, where both the above two equations are similar to the other two.

If there is a magnetic monopole, it behaves similarly to an electric field.

Step 2:

Thus, much as a magnetic field is created around a current-carrying wire, an electric field is created around a monopole current.

However, the direction of the electric field would be opposite to the magnetic field created by an electric field.

As a result, a new rule to determine the direction would be the left-hand rule. The left thumb is pointed in the direction of the monopole current, and the fingers are now coiled around it in the direction of the electric field.

Hence, an electric field is generated around a monopole current in the same way that a magnetic field is generated around a current-carrying conductor.