This question is from John Taylor, Classical Mechanics - Chapter 15, 109P. Two e

Question

This question is from John Taylor, Classical Mechanics - Chapter 15, 109P.

Two equal charges q are moving side-by-side in the positive x direction in frame S. The distance between them is r and their speed is v. Find the force on either charge due to the other in two ways:

(a) Find the force in their rest frame S' and transform back to S, using the force transformation (15.155) of Problem 15.83. Note that the force in S is less than in the rest frame.

(b) Find the electric and magnetic fields in S' and thence in S, using the field transformation (15.146). Use these fields (in S) and write down the Lorentz force on either charge in S. Note that in S there is an attractive electric force and a repulsive magnetic force. As beta -> 1 they become nearly equal and their resultant approaches zero.

Explanation / Answer

your answer is at [PDF] Solved Problems in Special Relativity - UBC Physics & Astronomy ... www.phas.ubc.ca/~mcmillan/rqpdfs/1_relativity.pdf

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