1. The problem statement, all variables and given/known data A small, thin coil with N2 loops, each of area A2, is placed inside a long solenoid, near its center. The solenoid has N1 loops in its length L and has area A1. Find the mutual inductance as a function of θ, the angle between the plane of the small coil and the axis of the solenoid. 2. Relevant equations M2 = N2[itex]\phi[/itex]2/I1 [itex]\phi[/itex]2 = BA2cos(θ) = μ0(N1/L)I1A2cos(θ) 3. The attempt at a solution If we just substitute for [itex]\phi[/itex]2 into the equation for M2, we get that M2 = (N2/I1)BA2cos(θ) = μ0(N1N2/L)A2cos(θ) Everything is right here except that the correct solution has sin(θ) instead of cos(θ). Why is that? Isn't the magnetic flux defined as a dot product?