Question

The S.I. unit of pole strength is
$
  A.{\text{ A}}{{\text{m}}^2} \\
  B.{\text{ Am}} \\
  {\text{C}}{\text{. A}}{{\text{m}}^{ - 1}} \\
  D.{\text{ A}}{{\text{m}}^{ - 2}} \\
 $

Answer 1

Hint: Here we will proceed by writing the formula for the pole strength. Then by using the formula of magnetic field we can derive S.I. unit of pole strength.

Complete step-by-step answer:
The ability of a magnetic pole to produce a magnetic field around it is called magnetic pole strength.
As we know that pole strength is the measure of the amount of force exerted by one of the poles of a magnet to a pole of another magnet. The force can be attraction or repulsion.
The magnetic field B due to a pole of strength p1 at a distance r from the pole is defined as the force per unit positive pole at that point that is The magnetic field in any direction is then given by the partial derivation of the potential in that direction.
 We know that, magnetic field is
$B = \dfrac{F}{m}$ (here b= magnetic field, F= force, m=pole strength)
Now it can also be written as,
$m = \dfrac{F}{B}$
Now F can also be written as $qvB$ because the force is perpendicular to both the velocity $v$ of the charge $q$ and the magnetic field $B$. The magnitude of the force is $F = qvB{\text{ sin}}\theta $ where $\theta $ is the angle < ${180^ \circ }$ degrees between the velocity and the magnetic field.
$m = \dfrac{{qvB}}{B}$
Now cancelling ‘B’ we get
$m = qv$ which in units is expressed as ‘Am’
Therefore, (B) is the correct option.

Note: Whenever we come up with this type of problem where we are asked to find out the unit of any quantity. Then we first write the to calculate the quantity after that we will try to derive the unit of the quantity with that formula. (here standard unit of pole strength)