# Inductance of a loop in a nonuniform magnetic field

1. May 4, 2008

### sfdevil

1. The problem statement, all variables and given/known data
A square loop made of wire with negligible resistance is placed on a horizontal frictionless table. The mass of the loop is m and the length of each side is b. a nonuniform vertical magnetic field B=B0(1+kx) exists in the region, where B0 and k are constants. The loo is given a quick push with initial velocity v along x-axis. The loop stops after a time interval T. Find the inductance of the loop.

2. Relevant equations

emf(ind) = -L*dI/dT
U=1/2*L*I^2
emf= -delta flux/delta t

3. The attempt at a solution

well, I am sort of in a loss for this one.
I tried to get the induced emf by finding dflux/dt:

flux
=integral ( B0*(1+kx) * b dX )
= b*B0*(b*2*k*x+b^2*k+2*b)/2

change of flux in regards with time = dphi/dx * dx/dt
= b^2*k*B0*v (because velocity= dx/dt)

so emf is b^2*k*B0

now Im not sure what to do, since the resistance is negligble and i cant find the current from it....

also the whole time interval thing, where does it come into play (kinematics ?)
and should I use conservation of energy here ?
1/2 * m * v^2 = 1/2 * L * I^2 ? for some reason I don't think its the right way