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5.Magnetism and Matter
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બંને ચુંબકની ડાઇપોલ મોમેન્ટ $M $ છે.બંને ચુંબકના લંબદ્રિભાજક પર કેન્દ્રથી $d$ અંતરે $P$ બિંદુએ ચુંબકીય ક્ષેત્ર કેટલું થાય?
A
$\frac{{{\mu _0}}}{{4\pi }}\frac{M}{{{d^3}}}$
B
$\frac{{{\mu _0}}}{{4\pi }}\frac{{M\sqrt 2 }}{{{d^3}}}$
C
$\frac{{{\mu _0}}}{{4\pi }}\frac{{2\sqrt 2 M}}{{{d^3}}}$
D
$\frac{{{\mu _0}}}{{4\pi }}\frac{{2M}}{{{d^3}}}$
Solution
(c)Resultant magnetic moment of the two magnets is
${M_{net}} = \sqrt {{M^2} + {M^2}} = \sqrt 2 M$
Imagine a short magnet lying along $OP$ with magnetic moment equal to $M\sqrt 2 $. Thus point $P$ lies on the axial line of the magnet.
$\therefore $ Magnitude of magnetic field at $P$ is given by $B = \frac{{{\mu _0}}}{{4\pi }}.\frac{{2\sqrt 2 M}}{{{d^3}}}$
Standard 12
Physics
