Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

Two very long straight-line charges (linear charge density lambda) are a distanc

ID: 1997802 • Letter: T

Question

Two very long straight-line charges (linear charge density lambda) are a distance d apart. Both move to the right at constant speed v. How big does v have to be so that the magnetic attraction exactly balances the electric repulsion? Find the actual number for the required v, and comment! Along with the necessary addition made by Maxwell, Ampere's law in full glory reads vector nabla times vector B = mu_0 vector J + 1 partial differential vector E/c^2 partial differential t. Take the divergence of this equation, and derive the continuity equation (Eq 5.29 in Griffiths section 5.1.3). You have just derived the conservation of electric charge!

Explanation / Answer

A) electrostatic force per meter = lamda/2pi eo d* lambda = lambda^2/2 pi eo d

magnetic force per meter = lambda vB = lambda*v* uo (lambda v)/2pid = lambda^2 v^2 uo/2pi d

Both has to be equal, 1/eod = uov^2/d

v = sqrt(1/eouo)

B) equation of Griffiths has to be given