Question

Two identical short bar magnets, each having magnetic moment of $10A{m}^2$, are arranged such that their axial lines are perpendicular to each other and their centres along the same straight line in a horizontal plane. If the distance between their centres is $0.2m$, the resultant magnetic induction at a point midway between them is $\left({\mu }_0=4\pi \times 10^{-7}H{m}^{-1}\right)$

• A. $\sqrt{2}\times 10^{-7}T$
• B. $\sqrt{5}\times 10^{-7}T$
• C. $\sqrt{2}\times 10^{-3}T$
• D. $\sqrt{5}\times 10^{-3}T$

Answer 1

Answer: (D)

From figure, $B_{net}=\sqrt{B_1^2+B_2^2}$
$=\sqrt{{\left(\frac{{\mu }_0}{4\pi }\cdot \frac{2M}{d^3}\right)}^2+{\left(\frac{{\mu }_0}{4\pi }\cdot \frac{M}{d^3}\right)}^2}$
$=\sqrt{5}\cdot \frac{{\mu }_0}{4\pi }\cdot \frac{M}{d^3}$
$=\sqrt{5}\times 10^{-7}\times \frac{10}{(0.1{)}^3}$
$=\sqrt{5}\times 10^{-3}T$