How Is Current Induced in a Circular Coil by a Changing Magnetic Field?

[fruitbubbles]

Homework Statement

. A circular coil of radius 5.0 cm and resistance 0.20 Ω is placed in a uniform magnetic field perpendicular to the plane of the coil. The magnitude of the field changes with time according to B = 0.50e-20t T. What is the magnitude of the current induced in the coil at the time t = 2.0 s?

Homework Equations

Φ = BAcos(0) = BA
emf = -dΦ_B /dt = -d(BA)/dt = -A * d(B)/dt

The Attempt at a Solution

I differentiated that magnetic field and got -10e^-20t, then multiplied that times pi*(.05²), and ultimately divided by .2 Ω. My answer is 1.66*10¹⁸, which is nowhere near any of the answers. I feel like I'm following a logical path but obviously this isn't working, so I don't know what else to do.

 

[Delta2]

Your mistake is that you don't take into account the self inductance L of the coil. It will be $E+L\frac{dI}{dt}+IR=0$ where E(t) exactly as you calculated and R=0.2Ohm. You still have to calculate L from the geometrical data of the coil and then solve the differential equation. In doing that becareful that E is not constant but varies with time as of course the current I(t) do so also.