If $B_{E}$ represents equatorial magnetic field and $B_{A}$ represents axial magnetic field due to a bar magnet. Which of the following relationships between $B_{E}$ and $B_{A}$ is correct?

B_{E} = 2 B_{A}

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B_{A} = 2 B_{E}

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B_{E} = 4 B_{A}

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B_{A} = 4 B_{E}

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Solution

The correct option is A $B_{A} = 2 B_{E}$
As equatorial magnetic field due to bar magnet is
$B_{E} = \frac{μ_{0} m}{4 π^{3}}$ .....(i)
and axial magnetic field due to bar magnet is
$B_{A} = \frac{μ_{0}}{4 π} \frac{2 m}{r^{3}}$ .... (ii)
From (i) and (ii), we get
$B_{A}$ = $2 B_{E}$

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