Question

Two identical short magnets having magnetic moment M are placed perpendicular to each other centres coinciding as shown in adjacent figure. The magnitude of the magnetic field at a point P at angle distance 'd' on the bisector of right angle will be :

• A. $\frac{\sqrt{2}{\mu }_{0}M}{4\pi d^3}$
• B. $\frac{2\sqrt{2}{\mu }_{0}M}{4\pi d^3}$
• C. $\frac{2{\mu }_{0}M}{4\pi d^3}$
• D. $\frac{\sqrt{3}{\mu }_{0}M}{4\pi d^3}$

Answer 1

The correct option is A $\frac{\sqrt{2}{\mu }_{0}M}{4\pi d^3}$

Both the fields are perpendicular to each other.
$\therefore B=\sqrt{B^2+B^2}=B\sqrt{2}$
$B=\frac{{\mu }_{0}M}{4\pi d^3}\sqrt{2}=\frac{\sqrt{2}{\mu }_{0}M}{4\pi d^3}$