Question

Two short bar magnets each of magnetic moment of $9A{m}^2$ are placed such that one is at $x=-3cm$ and the other at $y=-3cm$. 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)
$B_1=\frac{{\mu }_0}{4\pi }\times \frac{2M}{r^3}=10^{-7}\times \frac{2\times 9}{27\times 10^{-6}}$
$B_1=\frac{2}{3}\times 10^{-1}T$
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,
$B=\left(\frac{1}{3}+\frac{2}{3}\right)\times 10^{-1}T$
$\Rightarrow B=10^{-1}T=0.1T$