JEE MAIN - Physics (2020 - 3rd September Morning Slot - No. 8)
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 :
250$$\sqrt 3 $$
5$$\sqrt 3 $$
500$$\sqrt 3 $$
50$$\sqrt 3 $$
Explanation
_3rd_September_Morning_Slot_en_8_1.png)
$$\tan 30 = {x \over d}$$
$$d = {x \over {\tan 30}}$$
$$d = {{5 \times {{10}^{ - 2}}} \over {{1 \over {\sqrt 3 }}}}$$
$$d = 5\sqrt 3 \times {10^{ - 2}}$$
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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