Question

Two short bar magnets each of magnetic moment of $9\, Am ^{2}$ are placed such that one is at $x=-3\, cm$ and the other at $y=-3\, cm$. If their magnetic moments are directed along positive and negative $X$ -directions respectively, then the resultant magnetic field at the origin is

• A. 100T
• B. 10 T
• C. 0.1 T
• D. 0.001T

Answer 1

Answer: (C)

At origin, both magnetic fields will be in same direction.

Magnetic field due to $M_{1}$ (axial point)
$B_{1}=\frac{\mu_{0}}{4 \pi} \times \frac{2 M}{r^{3}}=10^{-7} \times \frac{2 \times 9}{27 \times 10^{-6}}$
$B_{1}=\frac{2}{3} \times 10^{-1} T$
Magnetic field due to $M_{2}$ (equatorial point)
$B_{2}=\frac{\mu_{0}}{4 \pi} \times \frac{M}{r^{3}}=10^{-7} \times \frac{9}{27 \times 10^{-6}}=\frac{1}{3} \times 10^{-1} T$
As both $B_{1}$ and $B_{2}$ points in same direction, so effective field,
$B=\left(\frac{1}{3}+\frac{2}{3}\right) \times 10^{-1} T$
$\Rightarrow B=10^{-1} T =0.1\, T$