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5.Magnetism and Matter
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A bar magnet of length $6\,cm$ has a magnetic moment of $4\,J\,T^{-1}$. Find the strength of magnetic field at a distance of $200\,cm$ from the centre of the magnet along its equatorial line.
A
$4\times 10^{-8}\,tesla$
B
$3.5\times 10^{-8}\,tesla$
C
$5\times 10^{-8}\,tesla$
D
$3\times 10^{-8}\,tesla$
(AIEEE-2012)
Solution
Along the equatorial line, magnetic field strength
$B = \frac{{{\mu _0}}}{{4\pi }}\frac{M}{{{{({r^2} + {l^2})}^{3/2}}}}$
Given: $M=4\, \mathrm{J} T^{-1}$
$r=200 \,\mathrm{cm}=2 \,\mathrm{m}$
$\ell=\frac{6 \,\mathrm{cm}}{2}=3\, \mathrm{cm}=3 \times 10^{-2}\, \mathrm{m}$
$\therefore B=\frac{4 \pi \times 10^{-7}}{4 \pi} \times \frac{4}{\left[2^{2}+\left(3 \times 10^{-2}\right)^{2}\right]^{3 / 2}}$
Solving we get, $B=5 \times 10^{-8}$ $tesla$
Standard 12
Physics
