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Space is divided by the line AD into two...

Space is divided by the line AD into two regions. Region I is field free and the Region II has a unifrom magnetic field B direction into the plane of the paper. ACD is a simicircular conducting loop of radius r with center at O, hte plane of the loop being in the plane of the paper. The loop is now made to rotate with a constant angular velocity `omega` about an axis passing through O and the perpendicular to the plane of the paper. The effective resistance of the loop is R.

(i) obtain an expression for hte magnitude of the induced cureent in the loop.
(ii) Show the direction of the current when the loop is entering into the Rigion II.
Plot a graph between the induced e.m.f and the time of roation for two periods or rotation.

Text Solution

Verified by Experts

When the loop is in region I, the magnetic field linked with the loop is zero. When the loop enters in magnetic field in region II. the magnetic flux linked with it, is given by`
phi=BA`
therefore e.m.f  induced`epsilon=`-(dphi)/(dt)=-(d(BA))/(dt)`Induced current =`(e.m.r)/(R)=(1)/(2)(Br^(2)0mega)/(R)`  dA can also be calculated in the following way: The area corresponding `2pi (angle)` is is`pi r^(2)`
therefore area corresponding to unit angle
area corresponding to angle `dtheta=(pir^(2))/(2r)xxdtheta` `therefore dA=(pi^(2))/(2r)xxdtheta=(1)/((2)r^(2)dtheta`
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