# 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$\pi a^2/ R$

asked Feb 9, 2017
I think you are correct $dq=d\phi /R$
English Lesson : "flown" is the past tense of "to fly". eg "The baby bird has flown the nest."  The past tense of "to flow" is "flowed".  eg "The electric charge which flowed in the circuit after the switch was closed was 3 Coulomb." Putting your title in the past tense makes it sound awkward : "Charge which flowed through circular loop." Putting it in the present tense sounds better : "Charge flowing through circular loop" or "Charge which flows through circular loop."

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.