# Electromagnetics: Moving loop in a static magnetic field

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1. Oct 30, 2015

### JasonHathaway

1. The problem statement, all variables and given/known data
A conducting square loop (L × L) moving with velocity vo ay m/s where the magnetic flux density is B=Bo ax Wb/m2 in 0 < y < 2L, and is equal to zero when 0 > y and y > L. Determine the current in the loop and plot its magnitude as a function in the loop's position in the y-axis. Assume the loop's front at y=0 and t=0 (time), and its resistance is R Ω.

2. Relevant equations
I=V/R (Ohm's law)
Vemf=u × B × dl (× refers to cross product, u is the velocity)

3. The attempt at a solution
Vemf=- vo B l V
I=Vemf/R = ( - vo B l )/ R A

I don't know whether I am doing OK or not. I feel like I've missed up with dl. Can anyone clarify?

2. Oct 31, 2015

### rude man

This formula is wrong, in fact, it's not a formula at all since you can't write "a x b x c". Plus, you're equating a differential quantity with a finite quantity. You need to be more careful with your vector math. But express V as a differential and fix your "u × B × dl" term, and you're there.
As for your "Vemf=- vo B l V", that is OK in magnitude but you need to get the vector formula right to determine the direction of the current. Or use Lenz's law.
And BTW V is not a vector.