# Induced emf at a specific time

1. Oct 28, 2009

### Liketothink

1. The problem statement, all variables and given/known data

A circular coil with 35 turns of wire and a diameter of 19 cm is placed in a magnetic field given by B(t) = 6 t^2 + 6 t + 2 T where t is time in seconds. The field is perpendicular to the plane of the coil. What is the induced EMF at t = 5 s?

2. Relevant equations

E=-d(magnetic flux)/dtime

3. The attempt at a solution
I found E to be 36.12 V but that's wrong. I'm not sure what's wrong. I did E=NAB/time.

Last edited: Oct 28, 2009
2. Oct 28, 2009

### Gear300

Emf is proportional to negative the derivative or rate of change of the magnetic flux with respect to time. The area is constant, thus
V = -NA*dB/dt.

3. Oct 28, 2009

### Liketothink

I plugged in -36.12 but it's still wrong. Can we have a negative voltage?

4. Oct 28, 2009

### Liketothink

Could you please tell me where I'm wrong? I have a couple of hours left.

5. Oct 28, 2009

### Gear300

dB/dt = 12t + 6; at t = 5s, dB/dt = 66T/s
N = 35 turns
A = pi*r^2...so your problem might be that you're using the diameter of 19cm instead of the radius; also, be sure that you convert the given units to the proper units, so the radius = d/2 = 9.5cm = .095m.
The emf is V = -NA*dB/dt....and you could have a negative voltage.

6. Oct 28, 2009

### Liketothink

Thank you very much I appreciate it.