Question

Two short bar magnets of magnetic moments $‘M^{\prime }$ each are arranged at the opposite corners of a square of side $‘d^{\prime }$ such that their centres coincide with the corners and their axes are parallel to one side of the square. If the like poles are in the same direction, the magnetic induction at any of the other corners of the square is.

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

Answer 1

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

Magntic field due to a dipole along axial and equatorial planes are
$B_0=\frac{2{\mu }_0}{4\pi }\frac{M}{r^3}$
$B_{90}=\frac{{\mu }_0}{4\pi }\frac{M}{r^3}$



Magntic field at point due to 1 is $B_1$ and due to 2 is $B_2$

Applying the formulas,
$B_1=\frac{{\mu }_0}{4\pi }\frac{M}{r^3}$ and
$B_2=\frac{2{\mu }_0}{4\pi }\frac{M}{r^3}$

$\therefore$ Net magnetic field at point $=B_2-B_1$
$=\frac{{\mu }_0}{4\pi }\frac{M}{d^3}$