Question

What is the magnitude of the equatorial and axial fields due to a bar magnet of length $5.0\, cm$ at a distance of $50\, cm$ from its mid-point? The magnetic moment of the bar magnet is $0.40\, Am ^{2}$.

• A. $3.2 \times 10^{-6} T , 6.4 \times 10^{-7} T$
• B. $4.2 \times 10^{5} T , 6 \times 10^{-7} T$
• C. $5 \times 10^{-6} T , 3.2 \times 10^{-7} T$
• D. $3.2 \times 10^{-7} T , 6.4 \times 10^{-7} T$

Answer 1

Answer: (D)

Magnetic field at equatorial line
$B_{E} =\frac{\mu_{0} m}{4 \pi r^{3}}=\frac{10^{-7} \times 0.4}{(0.5)^{3}}=\frac{10^{-7} \times 0.4}{0.125}$
$=3.2 \times 10^{-7} T$
Magnetic field at axial line $B_{A}=\frac{\mu_{0} 2 m }{4 \pi r^{3}}$
$=6.4 \times 10^{-7} T$