Magnetic scalar potential is defined as

Apply this equation to a closed curve enclosing a long straight wire. The RHS of the above equation is then –μ₀i by Ampere’s law. We see that even when . Can we have a magnetic scalar potential in this case?

Question

Magnetic scalar potential is defined as

Apply this equation to a closed curve enclosing a long straight wire. The RHS of the above equation is then –μ₀i by Ampere’s law. We see that even when . Can we have a magnetic scalar potential in this case?

Philoid · Accepted Answer

No, a magnetic scalar potential is not possible in this case.

The magnetic scalar potential, analogous to electric scalar potential, is calculated between two different point. But Ampere’s law is used for a closed, plane curve only.

For a straight long wire, the magnetic field is distributed surrounding the wire. In that case, if we calculate the magnetic potential by the given expression, over a closed curve, the beginning and the end points will coincide and the potential becomes zero.

Hence, In the given case, even though the RHS gives a non-zero value, it is not possible to have magnetic scalar potential.

Magnetic scalar potential is defined asApply this equation to a closed curve enclosing a long straight wire. The RHS of the above equation is then –μ0i by Ampere’s law. We see that even when . Can we have a magnetic scalar potential in this case?

Magnetic scalar potential is defined as

Apply this equation to a closed curve enclosing a long straight wire. The RHS of the above equation is then –μ₀i by Ampere’s law. We see that even when . Can we have a magnetic scalar potential in this case?