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.
emf(ind) = -L*dI/dT
emf= -delta flux/delta t
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:
=integral ( B0*(1+kx) * b dX )
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 I am not sure what to do, since the resistance is negligble and i can't 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
just thoroughly confused with this one. please help !