Two identical magnetic dipoles of magnetic moment $2 \mathrm{~A} \mathrm{~m}^{2}$ are placed at a se

Question

Two identical magnetic dipoles of magnetic moment $2 \mathrm{~A} \mathrm{~m}^{2}$ are placed at a separation of 2 m with their axis perpendicular to each other in air. The resultant magnetic field a midpoint between the dipoles is\

Professor PC Thomas Classes · Answer

\ Let point P be a midpoint between the dipoles. The point $P$ will be in end-on position with respect to one dipole and in broad-side on position with respect to the other.\ $	herefore \mathrm{B}_{1}=\frac{\mu_{0}}{4 \pi} \frac{2 \mathrm{M}_{1}}{\mathrm{r}_{1}^{2}}=\frac{10^{-7} 	imes 2 	imes 2}{(1)^{3}}=4 	imes 10^{-7} \mathrm{~T}$\ $\mathrm{B}_{2}=\frac{\mu_{0}}{4 \pi} \frac{\mathrm{M}_{2}}{\mathrm{r}_{2}^{2}}=\frac{10^{-7} 	imes 2}{(1)^{3}}=2 	imes 10^{-7} \mathrm{~T}$\ As $B_{1}$ and $B_{2}$ are perpendicular to each other, therefore the resultant magnetic field at point $P$ is\ $\mathrm{B}=\sqrt{\mathrm{B}_{1}^{2}+\mathrm{B}_{2}^{2}}=\sqrt{\left(4 	imes 10^{-7}ight)^{2}+\left(2 	imes 10^{-7}ight)^{2}}$\ $=10^{-7} \sqrt{16+4}$\ $=10^{-7} \sqrt{20}=2 \sqrt{5} 	imes 10^{-7} \mathrm{~T}$\