# Integration of V(t) using faraday's law

1. Mar 9, 2006

### ilovephysics

Ok the question is with a U-shaped conductor and a bar that slides across. There is a battery and a switch, the switch is open for a long time then closed at t=0. Im supposed to find the velocity as a function of time. Im mostly having trouble with the integration, i know the answer but i cant seem to integrate it right.

We have to integrate the first term from 0 to v, and the second from 0 to t

dv/(E-BLv) = (LB/mR)dt

E=voltage of battery
B=magnetic field
L=length of rod
R=resistance

i get to the formula above and then try u-substitution and i cant seem to get it right, could someone integrate this and show me? thanks

2. Mar 10, 2006

### dextercioby

Make the sub

$$E-Blv= u$$

You get

$$dv=-\frac{du}{Bl}$$

And i'm sure you know how the limits of integration transform...

Daniel.