A circular loop carrting a current a current I has wire of total length L. A uniform umagnetic field B exists parallel to the plane of the loop. (a ) find the trouque on the loop.(b) If the sme length of the wire is used to form a squar loop, what would be the torque? Which is larger?

Explanation

(a)

`L = 2pi r rArr r = (L)/(2pi)`
`M = i. pi r^(2) = i. pi ((L)/(2pi))^(2) = (iL^(2))/(4pi), o.`
`tau = M B sin theta, theta = 90^(@)`
`= M B = (i L^(2)B)/(4pi)`
(b)
`L = 4a rArr a = (L)/(4)`
`M' = i.a^(2) = i((L)/(4))^(2) = (iL^(2))/(16)`
`tau' = M'B sin theta, theta = 90^(@)`
`= M'B = (iL^(2)B)/(16 pi)`
`tau gt tau'`
Note: For given length, circles have maximum area.