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A rectangular loop of length l and bread...

A rectangular loop of length `l` and breadth b is situated in a uniform magnetic field of induction B with its plane perpendicular to the field as shown in the figure . Calculate the rate of change of magnetic flux and the induced emf if the loop is rotated with constant angular velocity `omega`
(a) about an axis passing through the centre and perpendicular to the loop.
(b) about an axis passing through the centre parallel to the breadth through angle `180^(@)` .

Text Solution

Verified by Experts

(a) The flux linked through the loop at any instant is
`phi = "BA cos" theta `
`= Blb cos theta` = Blb= constant.
`:`. Rate of change of magnetic flux is
`(dphi)/(dt)= (d)/(dt) (Blb) implies (dphi)/(dt)=0 `
Hence induced e.m.f `epsilon = (dphi)/(dt) =0` .

(b) when the loop is rotated through `180^(@)` about an axis passing through centre and parallel to breadth the change in magnetic flux
`dphi = -Blb- (Blb)= -2Blb`.
`:.` The induced e.m.f
`e=-(dphi)/(dt) implies e= +(2Blb)/(pi//omega)`
`implies e= (2Blbomega)/(pi)`
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