Question

Two short bar magnets with magnetic moments 400 ab-amp $c{m}^2$ and 800 ab-amp $c{m}^2$ are placed with their axis in the same straight line with similar poles facing each other and with their centres at 20 cm from each other. Find the force of repulsion.

Answer 1

${\overline{P}}_1=400$ at amp ${cm}^2$

${\overline{P}}_2=800$ at amp ${cm}^2$

dist. b/w centrest $=20cm$

$B_1=\frac{{\mu }_0}{4\pi }\left(\frac{{2M}_1}{r^3}\right)$

$F_2=M_2\frac{d{B}_1}{dr}=M_2\frac{d}{dr}(\frac{{\mu }_0}{4\pi }\times \frac{2M_1}{r^3})$

$=2M_1{M}_2\times \frac{{\mu }_0}{4\pi }(\frac{-1}{r^6}\times {3r}^2)$

$=\frac{-3M_1{M}_2}{2\pi }\times {\mu }_0\left(\frac{1}{r^4}\right)$

$=-3\times \frac{400\times 800\times 4\pi \times {10}^{-7}}{2\pi \times {\left(20\right)}^4}$

$F_2=12\times {10}^{-1}N$

$(-)ve$ sign the direction only.