Question

Two short magnets each of dipole moment M, are fastened perpendicularly at their centres. The magnitude of magnetic field at a distance d from the centre on the bisector of the right angle is

• A. $\frac{\mu_0}{4\pi}$ $\frac{2M\sqrt{2}}{d^3}$
• B. $\frac{\mu_0}{4\pi}$ $\frac{M}{d^3}$
• C. $\frac{\mu_0}{4\pi}$ $\frac{M\sqrt{2}}{d^3}$
• D. $\frac{\mu_0}{4\pi}$ $\frac{2M}{d^3}$

Answer 1

Answer: (A)

\frac{\mu_0}{4\pi}$$\frac{2M\sqrt{2}}{d^3}

Answer 2

Resultant magnetic moment of the two magnets is $M_R = \sqrt{M^2 + M^2} = M \sqrt{2}$ Imagine a short magnet lying along OP with magnetic moment equal to $M_R \, i.e. \, M\sqrt{2}$ Thus point P lies on the axial line of the magnet $\therefore$ Magnitude of magnetic field at P is given by, B = $\frac{\mu_0}{4 \pi} \frac{2M \sqrt{2}}{d^3}$ $\left( \because \, B_{axial} = \frac{\mu_0}{4 \pi} \frac{2M}{r^3} \right)$