Question

Two identical magnetic dipoles of magnetic moments $1.0A{m}^2$ each, placed at a separation of $2m$ with their axis perpendicular to each other. The resultant field at point midway between the 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 $\sqrt{5}\times {10}^{-7}T$

As the axes are perpendicular, mid point lies on axial ;line of one magnet and on equatorial line of other magnet.

$\therefore B_1=\frac{{\mu }_0}{4\pi }\frac{2M}{d^3}=\frac{{10}^{-7}\times 2\times 1}{1^3}=2\times {10}^{-7}$ and

$B_2=\frac{{\mu }_0}{4\pi }\frac{M}{d^3}={10}^{-7}$

Resultant field=$=\sqrt{{B_1}^2+{B_2}^2}=\sqrt{5}\times {10}^{-7}T$