Question 178: 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 :

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