# Faraday's Law and magnetic field

1. Oct 21, 2006

### erik-the-red

A coil containing N = 550 turns with radius r = 3.90 cm, is placed in a uniform magnetic field that varies with time according to $$B=(At + Bt^4)$$, where $$A = 1.05 \cdot 10^−2 {\rm T}/{\rm s}$$ and $$B = 3.00 \cdot 10^−5 {\rm T}/{\rm s}^{4}$$. The coil is connected to a resistor of resistance 640 Ohms, and its plane is perpendicular to the magnetic field. The resistance of the coil can be neglected.

Find the magnitude of the induced emf in the coil as a function of time. Write your answer as an expression in terms of the variables given in the problem.

I'm thinking that the derivative of magnetic flux can be written as the derivative of (BA). A is constant, so it's A multiplied by the derivative of B.

I get $$(A + 4Bt^3)(A)$$.

The induced EMF is the negative of that multiplied by N.

I typed that in, but it wasn't right.

What did I not consider?

Last edited: Oct 21, 2006
2. Oct 21, 2006

### CPL.Luke

the derivative of the flux with respect to time is going to be

n(area) (d B/dt)

or n*pi*r^2(A+4Bt^3)

I usually neglect the negative sign unless the problem allows you to define coordinates properly.

3. Oct 21, 2006

### erik-the-red

I see I did not use the radius for the area.

Thank you.