Question

Two identical short bar magnets, each having magnetic moment of $10\, Am ^{2}$, 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 $0.2\, m$, the resultant magnetic induction at a point midway between them is $\left(\mu_{0}=4 \pi \times 10^{-7} Hm ^{-1}\right)$

• 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, $B_{ net }=\sqrt{B_{1}^{2}+B_{2}^{2}}$
$=\sqrt{\left(\frac{\mu_{0}}{4 \pi} \cdot \frac{2 M}{d^{3}}\right)^{2}+\left(\frac{\mu_{0}}{4 \pi} \cdot \frac{M}{d^{3}}\right)^{2}}$
$=\sqrt{5} \cdot \frac{\mu_{0}}{4 \pi} \cdot \frac{M}{d^{3}}$
$=\sqrt{5} \times 10^{-7} \times \frac{10}{(0.1)^{3}}$
$=\sqrt{5} \times 10^{-3} T$