Regarding using the RHR, my thumb is in direction of motion (parallel to page), my index finger pointing along magnetic field (into or out of page), which leaves third finger for induced current pointing down like gravity or up - this doesnt seem right…
Does the direction my second finger points in indicate the literal direction of magnetic field at that point in space, or do I need to further use right hand rule or something for a circular path around the finger
My attempt: due to symmetry along x-axis, net E is only along x^hat.
dQ = λ dl = λ (R dθ)
for each dl, the x component of distance from dl to the origin is Rcos(θ)
Hence, E_x = \int_{-θ_0}^{θ_0} k(λ R dθ)/(Rcos(θ)^2 = kλ/R \int_{-θ_0}^{θ_0} sec(θ)^2 dθ = 2kλ/R tan(θ_0) along negative x^hat...