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A current I is flowing in a hexgonal coi...

A current I is flowing in a hexgonal coil of side a figure. The magnetic field induction at the centre O of the coil will be

A

`(sqrt(2) mu_(0)I)/(pi a)`

B

`(sqrt(3) mu_(0)I)/(pi a)`

C

`(2 pi a)/(sqrt(3)I)`

D

`(mu_(0)I)/(pi a)`

Text Solution

Verified by Experts

The correct Answer is:
B
Here `angle EOD = 60^(@)`
`angle EON = 30^(@) = angle NOD`
OE = OD = ED = a

`ON = OE cos 30^(@) = a xx (sqrt(3))/(2)`
Total magnetic field induction at O due to current through all the six sides of hexagon is
`B = 6 xx (mu_(o))/(4pi) xx (1)/(a (sqrt(3))/(2)) (sin 30^(@) + sin 30^(@))`
`B = (sqrt(3) mu_(o)I)/(pi a)`
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