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A coil in the shape of an equilateral tr...

A coil in the shape of an equilateral triangle of side 0.02 m is suspended from a vertex such that it is hanging in a vertical plane between the pole pieces of a permanent magnet producing a horizontal magnetic field of `5 xx 10^(-2) T.` Find the couple acting on the coil when a current of 0.1 A is passed through it and the magnetic field is parallel to its plane.

A

`0.866 xx 10^(-6) Nm`

B

`1.732 xx 10^(-4) Nm`

C

`0.422 xx 10^(-6) Nm`

D

`0.866 xx 10^(-2) Nm`

Text Solution

Verified by Experts

The correct Answer is:
A
Here l = 0.02m , `B = 5 xx 10^(-2) T, I = 0.1 A`
Area of the triangular coil
` A = 1/2 |vec I xx vecI | =1/2 (I xx I sin 60^@)`
` = 1/2 l^2 sin 60^@ = 1/2 (0.02m)^2 (0.865)= 1.732 xx 10^(-4) m^2`
(as angle between the sides of an equilateral triangle is `60^@` Couple acting on the coil , `tau - IAB cos alpha `
`= (0.1 A) (1.732 xx 10^(-4) m^2) (5 xx 10^(-2) T) cos 0^@`
` = 0.866 xx 10^(-6) Nm`
(`alpha 0^@` as magnetic field is parallel to the plane of the coil)
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