Question

ELECTROMAGNETISM; Griffiths 4th edition page. Magnetism as a relativistic phenomenon.

Why is v- greater than v+? Please provide a complete explanation.

Thanks

of magnetism.4 Suppose you had a string of positive charges moving along to the right at speed v. I'lI assume the charges are close enough together so that we may regard them as a continuous line charge λ. Superimposed on this positive string is negative one, proceeding to the left at the same speed v. We have, then, a net current to the right, of magnitude I 2λν. (12.75) 0 lU v, Meanwhile, a distance s away there is a point charge q traveling to the right at speed u u (Fig. 12.34a) Because the two line charges cancel, there is no electrical force on q in this system (S). However, let's examine the same situation from the point of view of system S, which moves to the right with speed u (Fig. 12.34b). In this reference frame q is at rest. By the Einstein velocity addition rule, the velocities of the positive and negative lines are now U干11 (12.76) Because v is greater than the Lorentz contraction of the spacing between negative charges is more severe than that between positive charges; in this frame, therefore, the wire carries a net negative charge! In fact, (12.77) where (12.78) 牲=

Answer 1

*. From figure( 12-1%a) , -He folc-hve changes moveicylela tothe right at sPeed V ohile ve changes move tohe e rH o di (tance, S , a Point change, g. maw eling, to -the- ruuve, iS Vu Hene VC Here V>a Thus VtV- Thus V V Vracten than V