Question

What is the value of magnetic potential, at a distance of 1cm from the pole, of pole strength 60Am?

A) 600 mJ/Am
B) 600 µJ/Am
C) 600 MJ/Am
D) 600 KJ/Am

Answer 1

Magnetic potential is work done by the bringing test pole from infinity to a particular distance r
$w = - \int\limits_\infty ^r {dv.dr}$. Since magnetic fields and displacement vectors are in opposite directions .

Step by step solution
we express the magnetic field B in a similar manner as the gradient of some potential function ψ, so that, for example, B = −grad ψ Before answering this, we note that there are some differences between E and B . Unlike E, the magnetic field B is sourceless; there are no sources or sinks; the magnetic field lines are closed loops. The force on a charge q in an electric field is qE, and it depends only on where the charge is in the electric field – i.e. on its position.

Thus the force is conservative, and we understand from any study of classical mechanics that only conservative forces can be expressed as the derivative of a potential function. The force on a charge q in a magnetic field is qv % B. This force (the Lorentz force) does not depend only on the position of the particle, but also on its velocity (speed and direction). Thus the force is not conservative. This suggests that perhaps we cannot express the magnetic field merely as the gradient of a scalar potential function

Let us considered following assumption
pole strength = P
distance where magnetic potential to be find = r meters= 1cm=.01m

We know that
Magnetic potential at distance r =${\mu _o}P \div 4\pi$
${V_r} = (4\pi \times {10^{ - 7}} \times 60) \div (4\pi \times .01) \\\ {V_r} = 6 \times {10^{ - 4}} = 600 \times {10^{ - 6}} = 600\mu J/Am \\\ \\\$

Option :B

Note: Magnetic potential is a dot product of two vectors . Hence it is considered to be a scalar quantity. The same question can be solved by a force method which includes vector addition .