Question

Two identical short bar magnets, euch having magnetic moment of $10A{m}^2$, are arranged such that their axial lines are perpendicular to each other and their centres be 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
$({\mu }_0=4\pi \times {10}^{-7}H{m}^{-1})$

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

Answer 1

Answer: (D)

$\sqrt{5}\times {10}^{-3}$tesla

From figure $B_{net}=\sqrt{B_a^2+B_e^2}$

=${\sqrt{{\left(\frac{{\mu }_0}{4\pi }\frac{2M}{d^3}\right)}^3+\left(\frac{{\mu }_0}{4\pi }\frac{M}{d^3}\right)}}^2$

=$\sqrt{5}.\frac{{\mu }_0}{4\pi }.\frac{M}{d^3}=\sqrt{5}\times {10}^{-7}\times \frac{10}{(0.1{)}^3}=\sqrt{5}\times {10}^{-3}Tesla$.