Qstnid -I-8-magnetic Scalar Potential Is Defined As Ur→2-ur→1=-∫r→1r→2b→.dl→apply This Equation To A Closed Curve Enclosing A Long Straight Wire. The Rhs Of The Above Equation Is Then -Μ<sub>0</sub> I By Ampere’s Law. We See That Ur→2≠ur→1even When R→2=r→1. Can We Have A Magnetic Scalar Potential In This Case? - 36: Permanent Magnets - Neet-xii-physics

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36: Permanent Magnets

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#8
Magnetic scalar potential is defined as
Ur→2-Ur→1=-∫r→1r→2B→.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
Ur→2≠Ur→1even when
r→2=r→1. Can we have a magnetic scalar potential in this case?
Ans : No, we cannot have a magnetic scalar potential here.
Ampere's law is a method of calculating magnetic field due to current distribution. On the other hand, magnetic scalar potential requires a magnetic field due to pole strength m.
Potential at a distance r is given by
`` \frac{{\mu }_{0}m}{4\,\mathrm{\,\pi \,}r}``
As there is no current distribution, no magnetic field due to poles or the pole strength is present. That is why we cannot have a magnetic scalar potential in this case.
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