1. The problem statement, all variables and given/known data Describe semiquantitatively the motion of an electron under the presence of a constant electric field in the x direction, E =E0x^ and a space varying magnetic field given by B = B0 a(x + z)x^ + B0 [1 + a(x - z)]z^ where Eo, Bo, and a are positive constants, lαxl « 1 and lαzl « 1. Assume that initially the electron moves with constant velocity in the z direction, v(t = 0) = v0z^. Verify if t his magnetic field satisfies the Maxwell equation ∇ x B = 0 2. Relevant equations Equation of motion: m dv/dt = q[E + v × B] 3. The attempt at a solution I've proven that the B field satisfies the Maxwell equation. and considering B(0,0,0) = B0 z^ I got the B field as a first order approximation about the origin as B(r) = B0z^ + (B0αx + B0αz)x^ + (B0αx - B0αz )z^ So from the equation of motion I get: m dv/dt = q[E + v × B] = q[E + v × B0 + v×[r⋅∇B]] The first two terms on the right hand side show that the particle would have a uniform acceleration along the x direction and a circular motion (varying with the instantaneous velocity) with x and y components; the last term is a force term and results in a combined gradient-curvature drift of the particle. I feel like I'm missing something regarding the divergent term of ∇B. How far should i go with the resolution of the equation of motion?