# Induced Voltage of Faraday's Disk

1. Feb 3, 2010

### Bizkit

1. The problem statement, all variables and given/known data
The problem can be found http://whites.sdsmt.edu/classes/ee382/homework/382Homework3.pdf" [Broken]. It is the first one.

2. Relevant equations
$$V_{emf} = \oint_L (\vec{\boldsymbol u} \times \vec{\boldsymbol B}) \cdot d\vec{\boldsymbol l}$$

3. The attempt at a solution
$$\vec{\boldsymbol u} = \rho\omega\hat{\boldsymbol a}_{\Phi}$$

$$\vec{\boldsymbol B} = B_0\hat{\boldsymbol a}_{z}$$

$$d\vec{\boldsymbol l} = d\rho\hat{\boldsymbol a}_{\rho}$$

$$\vec{\boldsymbol u} \times \vec{\boldsymbol B} = \rho\omega\hat{\boldsymbol a}_{\Phi} \times B_{0}\hat{\boldsymbol a}_{z} = \rho\omegaB_{0}\hat{\boldsymbol a}_{\rho}$$

$$V_{emf} = \oint_L(\vec{\boldsymbol u} \times \vec{\boldsymbol B}) \cdot d\vec{\boldsymbol l} = \oint_{L}\rho\omega B_{0}\hat{\boldsymbol a}_{\rho} \cdot d\rho\hat{\boldsymbol a}_{\rho} = \oint^{R}_{0}\rho\omega B_{0}d\rho = \omega B_{0}[\rho^{2}/2]^{R}_{0} = NB_{0}R^{2}/2$$

I'm pretty certain that this answer is correct. What I'm uncertain of is the polarity of the voltage. Should I add a minus sign in front, or leave it as is?

Last edited by a moderator: May 4, 2017