Question

Two short magnets of equal dipole moments M are fastended perpendicularly at their center as shown below (point P is the plane of the mangnets)
The magnetic field (magnitude) at P. distance d from the center 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. $\frac{{\mu }_0}{4\pi }\frac{2M\sqrt{2}}{d^3}$
• D. $\frac{{\mu }_0}{4\pi }\frac{2\sqrt{2M}}{d^2}$

Answer 1

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

Given

2 magnets of dipole moment M

They are kept perpendicular to each other

P is a point at distanced on perpendicular bisector on centre

Solution

Magnetic field of both magnets at P will be same an perpendicular to each other.

$B_1=B_2=\frac{{\mu }_{0}2M}{4\pi d^3}$

$B_{eff}=(B_1^2+B_2^2{)}^{\frac{1}{2}}$

Putting values

$B_{eff}=2^{\frac{1}{2}}\ast \frac{{\mu }_{0}2M}{4\pi d^3}$

The correct option is C