Question

the interaction between the magnetic fields produced by the magnet and the current in the wire produces forces on the magnet and wire. Compare these two factors

Answer 1

Let the length of the magnet be l and the magnetic moment be m and we have to find the magnetic field at a distance r,

$\overrightarrow{B_1}=\frac{\mu_o m}{4\pi(r^3)}$

Magnetic field due to the current carrying conductor,

$\overrightarrow{B_2}=\frac{\mu_o i}{2 \pi r}$

Hence, the force between the two magnetic pole

$F=\frac{B_1 B_2 A}{2\mu_o}$

Now, substituting the values,

$\Rightarrow F = (\frac{\mu_o}{2\pi})^2\frac{miA}{2r^4}N$