Question

Two magnetic poles are located 5 cm apart in air. If each pole has a strength of 5 mWb, find the force of repulsion between them.
1. \(\frac{1}{{{\pi ^2}}}N\)
2. \(\frac{{6250}}{{{\pi ^2}}}N\)
3. \(\frac{{625}}{{{\pi ^2}}}N\)
4. \(\frac{{62.5}}{{{\pi ^2}}}N\)

Answer 1

Correct Answer - Option 2 : \(\frac{{6250}}{{{\pi ^2}}}N\)

Concept:

Magnetic pole strength:

• It is a measure of the force exerted by one face of a magnet on a face of another magnet when both magnets are represented by equal and opposite poles.
• Symbol: m.

Units:

• There are two possible units for magnetic pole strength in SI units, depending on how the pole force is described.
• If you describe this as force per unit field B, then the SI unit is the ampere-meter (A m).
•  It can also be defined as the force per field of unit H, in this case, the unit SI is the weber (Wb).

Calculations:

Force of repulsion is given by \(F = \frac{{\mu \;{m_1}\;{m_2}}}{{\;4\;\pi \;{d^2}}}\)

Given B = 5 mWb.

B= μ H

H = B / μ

m₁ = m₂ = H = B / μ

therefore \(F = \frac{{\;\;{B^2}}}{{4\;\pi \;\mu \;{d^2}}}\)

μ = permittivity = 4π × 10^-7

F = ( 5 × 10^-3)² / (4 × π × 4π × 10^-7 × 25 × 10^-4)

F = 6250 / π²  N