Answer to Question #197712 in Electricity and Magnetism for Eylul

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,

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