Question 187: Magnetism and Matter

Question

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

$	an 30 = {x \over d}$
$d = {x \over {	an 30}}$
$d = {{5 	imes {{10}^{ - 2}}} \over {{1 \over {\sqrt 3 }}}}$
$d = 5\sqrt 3  	imes {10^{ - 2}}$
For one part of the wire with N turns,
$B = {{{\mu _0}IN} \over {4\pi d}}(\sin {	heta _1} + \sin {	heta _2})$
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 	imes 50} \over {4 	imes 5\sqrt 3  	imes {{10}^{ - 2}}}}} ight)\left( {2 	imes {1 \over 2}} ight)$
$ = 500\sqrt 3 \left( {{{{\mu _0}I} \over \pi }} ight)$

Answer

250$\sqrt 3 $

Answer

5$\sqrt 3 $

Answer

500$\sqrt 3 $

Answer

50$\sqrt 3 $

Magnetism and Matter

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 :

Choose the correct answer: