Question

Two short magnets of equal dipole moments M are fastened perpendicularly at their centre (figure 36-Q1). The magnitude of the magnetic field at a distance d from the centre on the bisector of the right angle is

(a) $\frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }}\frac{\mathrm{M}}{d^3}$
(b) $\frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }}\frac{\sqrt{2}\mathrm{M}}{d^3}$
(c) $\frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }}\frac{2\sqrt{2}\mathrm{M}}{d^3}$
(d) $\frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }}\frac{2\mathrm{M}}{d^3}$

Answer 1

(c) $\frac{{\mu }_0}{4\pi }\frac{2\sqrt{2}M}{d^3}$


Magnetic field (B₁) due to the short dipole A of dipole moment M at an axial point is given by,
${\overrightarrow{B}}_1=\frac{{\mu }_0}{4\mathrm{\pi }}\frac{2M}{d^3}...\left(1\right)$
Magnetic field (B₂) due to the short dipole B of dipole moment M at an axial point is given by,
${\overrightarrow{B}}_2=\frac{{\mu }_0}{4\mathrm{\pi }}\frac{2M}{d^3}...\left(2\right)$
Resultant magnetic field (B) will be,
B = $\sqrt{{B_1}^2+{B_2}^2}$
B = $\frac{{\mu }_0}{4\mathrm{\pi }}\frac{2\sqrt{2}M}{d^3}$