Answer Happy

Let's consider a charge q located a distance z above a plane of charge with charge density go in the z = 0 plane. Everything is at rest in the 'lab frame'. q 7 = 0 O (a) Find the fields generated by the sheet alone, E₁ and B₁, for z > 0 in the Lab frame ("L" for "Lab"). Ignore the fields from the point charge! (b) Find the force, FL, on the charge in the lab frame. (c) = Suppose we step onto a train car moving at a speed v vx, relative to the Lab frame. From this new reference frame (The Train frame, or “T”), what are the charge and Z
current densities on the z = 0 plane, σt and KŢ? Express you answer in terms of v, σ0, and the Lorentz contraction factor, y = (1 — v²/c²)-¹/². 9 V: vî - O (d) Using your results from (c), find the fields in the new reference frame, EȚ and BT, for z > 0. (You should again ignore the fields from the point charge - just compute the fields from the sheet.) (e) Find ET and By using the relativistic field transformation equations, and show that they agree with (d). (f) Find the force on the charge in this new reference frame, FT. Express you final answer in terms of the force in the lab frame, FL, and the Lorentz contraction factor, y.