Question

Two identical short magnetic dipoles of magnetic moments $1.0A{m}^2$ each, placed at a separation at 2m with their axes perpendicular to each other. The resultant magnetic field at a point midway between dipole is:

• A. $5\times {10}^{-7}T$
• B. $\sqrt{5}\times {10}^{-7}T$
• C. ${10}^{-7}T$
• D. $2\times {10}^{-7}T$

Answer 1

The correct option is B $\sqrt{5}\times {10}^{-7}T$

With respect to 1st magnet, P lies in end side-on position ∴$B_1=\frac{{\mu }_0}{4\pi d^3}\left(2M\right)$ --- (RHS)

With respect to 2nd magnet. P lies in broad side on position.

∴ $B_2=\frac{{\mu }_0}{4\pi d^3}\left(M\right)$--- (Upward)

$B_1={10}^{-7}\times 2\times \frac{1}{1}=2\times {10}^{-7}T,$

$B_2=\frac{B_1}{2}={10}^{-7}T$

As $B_1$ and $B_2$ are mutually perpendicular, hence the resultant magnetic field $B_R=\sqrt{B_1^2+B_2^2}=\sqrt{(2\times {10}^{-7}{)}^2+({10}^{-7}{)}^2}=\sqrt{5}\times {10}^{-7}T$