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 be 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 $({\mu }_0=4\pi \times {10}^{-7}H{m}^{-1})$

• 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

The correct option is D $\sqrt{5}\times {10}^{-3}$ Tesla


From figure $B_{net}=\sqrt{B_a^2+B_e^2}$
$=\sqrt{{(\frac{{\mu }_0}{4\pi }.\frac{2M}{d^3})}^2+{(\frac{{\mu }_0}{4\pi }.\frac{M}{d^3})}^2}$
$=\sqrt{5}.\frac{{\mu }_0}{4\pi }.\frac{M}{d^3}=\sqrt{5}\times {10}^{-7}\times \frac{10}{(0.1{)}^3}=\sqrt{5}\times {10}^{-3}Tesla$