The magnitude of the magnetic field due to a short bar magnet having a magnetic moment of \( 0.2\,\mathrm{A\,m^2} \), at a distance of 50 cm from the centre of the magnet on its axial line will be
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( 3.2 \times 10^{-7}\,\mathrm{T} \)
A short bar magnet behaves as a magnetic dipole. On its axial line, at a distance \( r \) much larger than its length,
\( \displaystyle B = \frac{\mu_0}{4\pi}\,\frac{2m}{r^{3}} \)
\( \mu_0/4\pi = 10^{-7}\,\mathrm{T\,m\,A^{-1}} \)
\( r = 50\,\mathrm{cm} = 0.5\,\mathrm{m} \)
\( r^{3} = 0.125\,\mathrm{m^{3}} \)
\( \displaystyle B = 10^{-7} \times \frac{2 \times 0.2}{0.125} = 10^{-7} \times 3.2 = 3.2\times10^{-7}\,\mathrm{T} \)