II. PROBLEM 2. LIÉNARD-WIECHERT POTENTIALS.Problem 10.15A particle of charge q moves in a circle of radius a at constantangular velocity w. (Assume that the circle lies in the xy plane, centered at theorigin, and at time t = 0 the charge is at (a, 0), on the positive x axis.) Find theLiénard-Wiechert potentials for points on the z axis.It would be useful to parameterize the circle asr(t) = a (cos (wt) + sin (wt)ÿ),(1)2and then directly substitute the values into the Eqs. (10.46) and (10.47), i. e.V (r, t) =A(r,t) =V(r,t),(2)4TE0 2c - 4 vwhere|r – w (t,)|2 =r - w (t,), t, =t -=t -(3)and the velocity of the particle is also taken at the retarded time.

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Answered: Problem 10.15A particle of charge q…

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Problem 10.15A particle of charge q moves in a circle of radius a at constant angular velocity w. (Assume that the circle lies in the xy plane, centered at the origin, and at time 1 = 0 the charge is at (a, 0), on the positive x axis.) Find the Liénard-Wiechert potentials for points on the z axis.