Question

e. [1 pt] Now suppose we see that the particle is moving in a straight line, as shown in Figure 1. Find vq in terms of vx and physical constants. Can this be observed in a lab? (Recall that Eouoc2, nothing can travel faster than the speed of light, and that it costs an infinite amount of energy to accelerate something with nonzero mass up to the speed of light, c 3 x 108 m/s 109 miles per hour.) 0 0 Figure 1: Diagram of the system. The solid black line is the infinite line charge with charge density X. The origin of the coordinate system and directions of basis vectors and ż are also shown. In part a, you need to choose a direction for y such that the coordinates are right-handed. Parts b and c ask you to consider the electromagnetic field at some point rs, marked with a cross. Parts d onward analyse a charge at that location, shown in blue. Its hypothetical trajectory is the blue dashed line. f. [2 pt] If instead of a line of charge density A, we had an infinite sheet of charge density σ in the y-z plane moving with velocity też, what would the electric and magnetic fields be now? What Ampèran loop would we need to take? Make another diagram. (Recall Quiz 1)

Answer 1

At location of q F_E vector = qE vector = q Lambda/2 pi E_0 r x^F_B vector = q(v_q z^Times mu_0 I/2 pi r y^= -q v_q mu_o Lambda u lambda/2 pi r x^F_E vector + F_B vector = 0 NET ACCELATION ZERO q Lambda/ 2pi E_0 r = q V_q mu_0 Times Lambda V_Lambda/2 pi r (CONT VELOCITY) q Lambda/2 pi E_0 r/q mu_0 lambda u Lambda/2 pi r = v_q v_q = q lambda/2 pi E_0 r 2 pi r/ q mu_0 Lambda v Lambda = 1/E_0 mu_0 v Lambda v_q = c^2/ v lambda c^2 = 1/mu_0 E_0 because v Lambda < c V_q > c