Faraday's Law help, not sure if I'm using the equations correctly.

[beanus]

Homework Statement

A coil 3.55 cm radius, containing 480 turns, is placed in a uniform magnetic field that varies with time according to B = (1.20e-2 T/S)t + (3.05e-5 T/s^{4} )t^{4}. The coil is connected to a 620 Ohm resistor, and its plane is perpendicular to the magnetic field. You can ignore the resistance of the coil.

Homework Equations

\Phi_{B}=BA
ε = - \frac{\Phi_{B}}{t}

The Attempt at a Solution

First I divided by t and removed a t from each term in "B"

r = .0355
N = 480

A = \pi(.0355)^{2} = 3.959192142e-3
AN = (3.959192142e-3)(480) = 1.900412228

So all we're left with is:
BAN = 1.900412228 [(1.20e-2 T/S) + (3.05e-5 T/s^{3} )t^{4}]

ε = (2.28e-2 V) + (5.80e-5 V/s^{3})t^{3} should be my final answer but mastering physics says I'm wrong. Please help thanks!

EDIT:

I just found a posting where they multiplied the second term in B (3.05e-5 T/s^{3} )t^{4} by 4. When I did that I got the correct answer! But I don't know why I would multiply the term by 4. Any thoughts?

 

[technician]

I have not checked all of your maths but did you remember to x4 when you differentiated t^4 ??

 

[Redbelly98]

ε = - \frac{\Phi_{B}}{t}

ε = -\frac{d \Phi_{B}}{dt}, \ \text{ not } \ - \frac{\Phi_{B}}{t}