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Two identical short bar magnets, each having magnetic moment of $10\, Am^2$, are arranged such that their axial lines are perpendicular to each other and their centres be along the same straight line in a horizontal plane. If the distance between their centres is $0.2 \,m$ , the resultant magnetic induction at a point midway between them is$({\mu _0} = 4\pi \times {10^{ - 7}}\,H{m^{ - 1}})$
$\sqrt 2 \times {10^{ - 7}}$ $Tesla$
$\sqrt 5 \times {10^{ - 7}}$ $Tesla$
$\sqrt 2 \times {10^{ - 3}}$ $Tesla$
$\sqrt 5 \times {10^{ - 3}}$ $Tesla$
Solution
(d)From figure ${B_{net}} = \sqrt {{B_a}^2 + {B_e}^2} $
$ = \sqrt {{{\left( {\frac{{{\mu _0}}}{{4\pi }}.\frac{{2M}}{{{d^3}}}} \right)}^2} + {{\left( {\frac{{{\mu _0}}}{{4\pi }}.\frac{M}{{{d^3}}}} \right)}^2}} $
$ = \sqrt 5 .\frac{{{\mu _0}}}{{4\pi }}.\frac{M}{{{d^3}}}$$ = \sqrt 5 \times {10^{ – 7}} \times \frac{{10}}{{{{(0.1)}^3}}}$= $\sqrt 5 \times {10^{ – 3}}$ $Tesla$.
