# Calculating the EMF in the coil while the field is changing

1. Mar 29, 2017

### Ly444999

1. The problem statement, all variables and given/known data
A coil with 200 turns of wire is wrapped on an 18.0 cm square frame. Each turn has the same area, equal to that of the frame, and the total resistance of the coil is 2.0Ω . A uniform magnetic field is applied perpendicularly to the plane of the coil. If the field changes uniformly from 0 to 0.500 T in 0.80 s, find the magnitude of the induced emf in the coil while the field has changed

2. Relevant equations
emf =N* (Δ(BAcosθ) / Δt)

3. The attempt at a solution
I'm having trouble understanding the answer to the problem. In a solution to this question I seen, the answer is gotten from doing this calculation:
emf = [(200)*(0.500-0)*(0.18*0.18)*cos 90] / 0.80
and the answer equals to 4.10 V.
What I don't understand is why do you multiply by the cos 90?
cos 90 in degrees is 0 and in radians it is -0.4480736....
Doing the calculation without the cos 90 will get that answer, so why is it in the equation?

2. Mar 29, 2017

### Staff: Mentor

You need to make sure that you're using the correct angle. Check your notes or text to see when the angle is used and what it is the angle between.

Although you will find that the actual angle involved won't be 90°, note that 90° is equivalent to $\pi/2$ radians, and they are in fact the same angle and have the same cosine value: zero.

3. Mar 29, 2017

### Ly444999

So would no angle at all be used in this case?

4. Mar 29, 2017

### Staff: Mentor

There's an angle, but thanks to the particular geometry specified for the problem it has a value that doesn't affect the calculated result. You should make sure that you understand what that angle actually represents.

5. Mar 29, 2017

### Ly444999

I'm not sure if I'm following but, since the magnetic field is applied perpendicularly to the plane of the coil, the angle is actually 0 instead of 90?

6. Mar 29, 2017

### Staff: Mentor

Yes.

7. Mar 29, 2017