1. The problem statement, all variables and given/known data I am using these variables: L for the square length - so the rectangle on the left is L/2 by L B' = rate at which field increases λ = Resistance/Length I1 = Current on the right (so the top/right/bottom of square) - goes counterclockwise I2 = Current on the left (so the far left and the top/bottom on the little rectangle piece) - counterclockwise I3 = current through the middle wire (what the question is asking for) - unknown direction, I assumed downwards 2. Relevant equations V = IR Induced emf = derivative of flux flux = ∫ B dA 3. The attempt at a solution I have tried setting up loop-rule equations and then just using matrices to calculate the values of I. Loop rule for the square: V = B' * L2 = I1 * 3Lλ + I3 * Lλ Loop rule for the whole outer rectangle V = B' * 1.5 * L2 = I1 * 3Lλ + I2 * 2Lλ Loop rule for the left rectangle: V = B' * .5 * L2 = I2 * 2Lλ + I3 * Lλ Using the sum of currents in = sum of currents out I1 = I2 + I3 So I got 4 equations. I remember from non-magnetic field type circuit analysis questions with 3 unknown currents I had to use 2 voltage equations + sum of current equations, because the 3 voltage equations would not give enough information to solve the system. My guess is that any 2 voltage equations and the current equation would be all I need. I am getting the wrong answer with this set-up. Is there an error with my equations, or is this the completely wrong approach?