Electron Motion Near Current-Carrying Wire in Two Reference Frames · RMPH 2016 #2

Physics · electromagnetism

Problem

In a vacuum chamber there is a long, straight wire of negligible thickness made from a material with high electrical conductivity. An electrical current with the intensity of I=10AI = 10 A passes through the wire. Electrons are sent on a direction perpendicular on the wire, towards the wire. Their motion starts at the distance r0r_0 from the wire, with an initial speed v0v_0 much smaller than speed of light. The electrons cannot approach the wire at a distance less than r0/2r_0/2. Consider two reference frames – one being the laboratory system S.L. and the other being a mobile system S.M. that runs parallel to the wire with a constant speed v0v_0 in the direction in which the current flows through the wire. Neglect the magnetic field of Earth. 2.i. Deduce the expressions of induction of the magnetic field produced by the current flowing through the wire in each of the two reference frames B⃗S.L.(r)\vec{B}_{S.L.}(r), B⃗S.M.(r)\vec{B}_{S.M.}(r). (1.00p) 2.ii. Determine the expression of the difference between Lorentz forces in the two reference systems, F⃗S.L.(r)−F⃗S.M.(r)\vec{F}_{S.L.}(r) - \vec{F}_{S.M.}(r), forces acting on the electron sent to the wire. Express the result in terms of ee, μ0\mu_0, II, rr and v0v_0. (1.50p) 2.iii. State the values of the electron velocity's v(r0/2)v(r_0/2) components in both reference frames. (1.00p) 2.iv. Determine the expression of the speed v0v_0 as function of ee, mm, II, μ0\mu_0. Calculate the numerical value of v0v_0. (1.50p) 2.v. Deduce the expression of the maximum distance from the wire DD at which one can find the electron, as function of r0r_0, when the electron moves away from wire on a direction perpendicular on it. (0.50p)

Browse the problem library