Magnetic field in a region is equal to B. A loop of resistance R and radius r is lying in the field with the plane perpendicular to the field if the loop is turned by 180 degree. Find the charge which flows through a given cross section of the loop

Dear Student,

Please find below the solution to the asked query:

The emf generated by in the loop due to magnetic field is ε=-dϕdt=-ddtBAcosωt=BAωsinωt
Now if r is the radius of the loop then area is given by A=πr2
If I is the current through the loop we, then we have I=εR=Bπr2ωcosωtR
So total charge flown through the circuit is given by 
q=0TIdt=0TBπr2ωsinωtRdt
Here we are considering that the time taken to rotate 180 degree is T. Now we have
θ=ωtdθ=ωdt
Using above value we get
q=0πBπr2Rsinθdθ=Bπr2R0πsinθdθ=Bπr2R2=2Bπr2R


Hope this information will clear your doubts about this topic.

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