Question

Two short bar magnets of magnetic moments $m$ each are arranged at the opposite corners of a square of side d such that their centres coincide with the corners and their axes are parallel. 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_{0}}{4\pi} \frac{m}{d^{3}}$
• B. $ \frac{\mu_{0}}{4\pi} \frac{2m}{d^{3}}$
• C. $ \frac{\mu_{0}}{4\pi} \frac{m}{2d^{3}}$
• D. $ \frac{\mu_{0}}{4\pi} \frac{m^3}{2d^{3}}$

Answer 1

Answer: (A)

Magnetic induction at point $E$ due to magnet at $F$ (axial point) is
$B_{1} = \frac{\mu_{0}}{4\pi} \frac{2m}{d^{3}}$
It acts along $EF$.
Magnetic induction at point $E$ due to magnet at $D$ (equatorial point) is
$B_{2} = \frac{\mu_{0}}{4\pi} \frac{m}{d^{3}}$
It acts along $FE$.
Resultant magnetic induction at point $E$ is
$B = B_{1} - B_{2} = \frac{\mu_{0}m}{4\pi d^{3}}$