Question

Two short magnets of equal dipole moments M are fastened perpendicularly at their centre (figure). The magnitude of the magnetic field at a distance d from the centre on the bisector of the right angle is

• A. $\frac{{\mu }_0}{4\pi }\frac{M}{d^3}$
  
• B. $\frac{{\mu }_0}{4\pi }\frac{M\sqrt{2}}{d^3}$
  
• C. $\frac{{\mu }_0}{4\pi }\frac{2\sqrt{2}M}{d^3}$
• D. $\frac{{\mu }_0}{4\pi }\frac{2M}{d^3}$

Answer 1

The correct option is C $\frac{{\mu }_0}{4\pi }\frac{2\sqrt{2}M}{d^3}$

Resultant magnetic moment of the two magnets is
$M_{net}=\sqrt{M^2+M^2}=\sqrt{2}M$



Imagine a short magnet lying along OP with magnetic moment equal to $M\sqrt{2}$ . Thus point P lies on the axial line of the magnet.
$\therefore$ Magnitude of magnetic field at P is given by $B=\frac{{\mu }_0}{4\pi }.\frac{2\sqrt{2}M}{d^3}$