# Calculating EMF and flux rule

1. Dec 8, 2011

### randomafk

Hi,

I'm currently reading griffiths and I'm a little bit confused in how it calculates emf.

EMF is initially introduced as a path integral of force/unit charge around a closed loop. This makes sense, but then he presents us with an example problem (ex 7.4)

Basically, a circuit resistor is attached to a rotating metal disc normal to a uniform magnetic field at its edge and center. (fig 7.14)

He calculates emf as the line integral of the $∫f_{mag}ds$ from 0 to R of the disc. However, doesn't the current flow across the entire disc? Why would we still take a line integral -- shouldn't it be a surface integral across the disc? He says this makes the flux rule difficult since it assumes current alonga well-defined path. But doesn't that apply to calculating emf as well?

When we calculated voltage with an electric field, we do a line integral but it becomes a volume integral w.r.t to the volume in question. Is there any sort of analog here?

Thanks!