# Charge flown through circular loop

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A uniform but time varying magnetic field B = Kt – C ; (0 < t < C/K), where K and C are constants and t is time, is applied perpendicular to the plane of the circular loop of radius ‘a’ and resistance R. Find the total charge that will pass around the loop.

Flux =(Kt-c)$\pi a^2$
EMF=d(flux)/(dt)
=k$\pi a^2$
Current =k$\pi a^2$/R
So the charge flown through it hould be =k$\pi a^2$t/R

But the answer given as C$\pi a^2/ R$

I think you are correct $dq=d\phi /R$
You have not taken the final step. The experiment starts at $t=0$ and ends at $t=C/K$. The time for which the current flows is $t=C/K$. Substitute for $t$ into the formula for charge, then you have the correct answer.