Question

4. Field transformations: In the lab frame E 4 V/m, B -3y T, and a point charge q = 1C is observed to be moving with velocity v 2 m/s. a) What is the electric field E' measured in the frame of reference of q? Determine E' by ensuring that the Lorentz force applied on charge q is identical in both reference frames. b) Is this charge being accelerated or not under the influence of fields E and B? Discuss 5. Electrodynamics: Consider Newton's 2nd Law "F = ma" with F = q(E+ v x B) and acceleration = , applied to a charged particle with space and time) vector fields perpendicular to one another everywhere, then the solution of "F = ma" mass m, charge q, velocity v. If E and B are constant (in for v will contain a zero-average time-varying "AC" component as well as a "DC" component. For such a field configuration a) Determine the DC component of the velocity v of the particle assuming that v has a zero component parallel to B at t = time t in which case time average of "F ma" reduces to E + vDC X B = 0 for the given fields (2) you may need to use the vector identity A x (B x C) = (C A)B - (B - A)C on solving E vDC x B = 0 for vpc b) What is vDc found in (a) explicitly if E 2i V/m and B lỹ T? 0. Hint: (1) DC component vDC of v will be independent of VDC c) Bonus problem: How would the answer to parts (a) and (b) change if the particle had an initial velocity v = 2B/|B| m/s at time t = 0 in the direction parallel to the magnetic field vector B? Justify your answer d) Bonus problem: If an equal mix of positive and negative charge carriers per unit volume in the region were to move with the steady-state velocities implied by the result of (a), would the resulting charge carrier motions in the mix produce a net current density to the direction of B? Explain! Hint: for simplicity, assume that initial value of v parallel to B is zero flowing perpendicular

Answer 1

Solution:

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