1. The problem statement, all variables and given/known data Consider an infinite sheet of magnetized tape in the x-z plane with a nonuniform periodic magnetization M = cos(2πx/λ), where λ/2 is the distance between the north and south poles of the magnetization along the x-axis. The region outside the tape is a vacuum with no currents or time varying fields anywhere in space. Assume that the top surface of the tape is at y=0 and the B-field at the top is B= B_0[(y-hat)*sin(2πx/λ) -(x-hat)*cos(2πx/λ)]. a) Show that the H field in vacuum is given by a scalar potential H =-∇Φ. b) Find the most general Φ by solving Laplace's equation. c) State the boundary conditions on B and H, at y=0 and y=∞, necessary to find B in vacuum. d) Find B in the vacuum by the results of b) and c). e) A hydrogen atom of magnetic moment μ(y-hat) approaches the tape from above along x=3λ/4. Find the force on the atom as function of distance from the tape. Does the tape attract or repel this atom? 2. Relevant equations F= -∇(μ⋅B), ∇⋅H =-∇⋅M, Δ(∂Φ/∂r) =ΔM 3. The attempt at a solution a) The region outside the tape has no currents so ∇xH = ∇⋅H =0 ⇒ H= -∇Φ since ∇x(∇) =0. Therefore Φ satisfies Laplace's equation in 2-D. b) In polar coordinates the general solution is Φ(r,θ) =∑ (A_l r^l + B_l /r^[l+1]) P_l (cosθ). c) The potential must be continuous at the boundary and finite everywhere. The condition on H is the third relevant equation. d) Here I get stuck and am not sure how to use the boundary conditions. e) After finding B from d) we can use the first relevant equation to find the force on the atom.