QJEEM20Ph33e7: JEE Main 2020 Physics - Class 12 JEEM20Ph33e7 Solution: Magnitude of magnetic field (in SI units) at the centre of a…

Question

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Magnitude of magnetic field (in SI units) at the centre of a hexagonal shape coil of side 10 cm, 50 turns and carrying current I (Ampere) in units of

{{{\mu _0}I} \over \pi }

is :

Accepted Answer

\tan 30 = {x \over d}

d = {x \over {\tan 30}}

d = {{5 \times {{10}^{ - 2}}} \over {{1 \over {\sqrt 3 }}}}

d = 5\sqrt 3 \times {10^{ - 2}}

For one part of the wire with N turns,

B = {{{\mu _0}IN} \over {4\pi d}}(\sin {\theta _1} + \sin {\theta _2})

For 6 identical parts of the wire,

{B_{net}} = 6B

= {{6{\mu _0}IN} \over {4\pi d}}(\sin 30 + \sin 30)

= {{{\mu _0}I} \over \pi }\left( {{{6 \times 50} \over {4 \times 5\sqrt 3 \times {{10}^{ - 2}}}}} \right)\left( {2 \times {1 \over 2}} \right)

= 500\sqrt 3 \left( {{{{\mu _0}I} \over \pi }} \right)

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