Question

Magnetic scalar potential is defined as
U(→r2)-U(→r1)=-∫→r2→r1→B.→dl
Apply this equation to a closed curve enclosing a long straight wire. The RHS of the above equation is then −μ0 i by Ampere's law. We see that U(→r2)≠U(→r1)even when →r2=→r1. Can we have a magnetic scalar potential in this case?

Answer 1

No, we can’t have a magnetic scalar potential here.

Explanation:

• This is because ampere's law is a type of magnetic field measurement due to current distribution.
• On the other hand, due to pole strength m, magnetic scalar potential calls for a magnetic field.
• Potential at a distance r , $\frac{\mu_{0} m}{4 \pi r}$  is given  
• As there is no current distribution, there is no magnetic field due to poles or the force of the pole. Therefore in this case we cannot have a magnetic scalar potential.