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)

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