CALC Positive charge Q is distributed uniformly along the

Chapter 21, Problem 89P

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CALC Positive charge Q is distributed uniformly along the x-axis from x = 0 to x = a. A positive point charge q is located on the positive x-axis at x = a + r, a distance r to the right of the end of Q (Fig. P21.89).

(a) Calculate the x- and y-components of the electric field produced by the charge distribution Q at points on the positive x-axis where x > a.

(b) Calculate the force (magnitude and direction) that the charge distribution Q exerts on q.

(c) Show that if r >> a, the magnitude of the force in part (b) is approximately \(Q q / 4 \pi \epsilon_{0} r^{2}\). Explain why this result is obtained.