A coil 4.35 cm radius, containing 580 turns, is placed in a uniform magnetic fie

Question

A coil 4.35 cm radius, containing 580 turns, is placed in a uniform magnetic field that varies with time according to B = (1.20 times 10^-2 T/s)t + (3.05 times 10^-5 T/s^4)t^4. The coil is connected to a 640-ohm resistor, and its plane is perpendicular to the magnetic field. You can ignore the resistance of the coil. Find the magnitude of the induced emf in the coil as a function of time. epsilon = 1.32 times 10^-2 V + (1.34 times 10^-4 V/s^3)t^3 epsilon = 4.14 times 10^-2 V + (1.05 times 10^-4 V/s^3)t^3 epsilon = 4.14 times 10^-2 V + (4.21 times 10^-4 V/s^3)t^3 epsilon = 1.32 times 10^-2 V + (4.21 times 10^-4 V/s^3)t^3 What is the current in the resistor at time t_0 = 4.90 s? I = A

Explanation / Answer

we know that

emf = -dflux/dt

and flux=B*area where area is fixed

so emf=(dB/dt)*area

So derivative of it will give= n*(1.20*10-2) + 4*(3.05*10-5)t3*pi*0.04352

where n=580 gives option C the right answer

By ohms law

Current=emf/ressitence here R=640 ohm

so at t=4.90 s

Current=(4.14*10-2+(4.21*10-4)*4.93)/640= 1.4208*10-4 amp

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