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

Given,

Magnetic dipole moment is $M$

Distance is $d$

Let magnetic field of magnets are $B_1$ and $B_2$ and its resultant is $B$

Now,

$B_1=\frac{{\mu }_0}{4\pi }\frac{2M}{d^3}$

And

$B_2=\frac{{\mu }_0}{4\pi }\frac{2M}{d^3}$

$B=\sqrt{{B_1}^2+{B_2}^2}$

$=\sqrt{2{\left(\frac{{\mu }_{0}M}{4\pi d^3}\right)}^2}$

$=\frac{{\mu }_0}{4\pi }\frac{\sqrt{2}M}{d^3}$

Correct option is C.