# Faraday's Law of Induction

1. Apr 1, 2007

### AznBoi

1. The problem statement, all variables and given/known data
A wire loop of radius 0.3m lies so that an external magnetic field of magnitude 0.30 T is perpendicular to the loop. The field reverses its direction, and its magnitude changes to 0.20 T in 1.5s. Find the magnitude of the average induced emf in the loop during this time.

2. Relevant equations
$$\varepsilon_{avg} = \frac{-\Delta \Phi_{B}}{\Delta t}$$

$$\Phi_{B}=BAcos \theta$$

3. The attempt at a solution
$$A=\pi r^{2}=\pi (0.30m)^{2}= 0.09\pim^{2}$$

$$0s: \Phi_{B}=BA cos \theta =(0.30T)(0.09\pi m^{2}) = 0.0848 T*m^{2}$$

$$1.5s: \Phi = -(0.20T)(0.09\pi m^{2})= -0.05655 T*m^{2}$$

$$\varepsilon_{avg}=\frac{(-0.05655-0.0848)}{1.5s}=-0.14135$$

The correct answer, however, is 94 mV??

Last edited: Apr 1, 2007
2. Apr 1, 2007

### AznBoi

Nvm, I found my mistakes. Just some arithmetic errors :grumpy: