Introduction to Electrodynamics · Problem 10.28

Potentials and Fields — David J. Griffiths

Physics · lienard-wiechert-fields

Problem

One particle, of charge q1q_1, is held at rest at the origin. Another particle, of charge q2q_2, approaches along the xx axis, in hyperbolic motion: x(t)=b2+(ct)2;x(t) = \sqrt{b^2 + (ct)^2}; it reaches the closest point, bb, at time t=0t = 0, and then returns out to infinity. (a) What is the force F2F_2 on q2q_2 (due to q1q_1) at time tt? (b) What total impulse (I2=∫−∞∞F2 dt)\left(I_2 = \int_{-\infty}^{\infty} F_2\, dt\right) is delivered to q2q_2 by q1q_1? (c) What is the force F1F_1 on q1q_1 (due to q2q_2) at time tt? (d) What total impulse (I1=∫−∞∞F1 dt)\left(I_1 = \int_{-\infty}^{\infty} F_1\, dt\right) is delivered to q1q_1 by q2q_2? [Hint: It might help to review Prob. 10.17 before doing this integral. Answer: I2=−I1=q1q2/4ϵ0bcI_2 = -I_1 = q_1 q_2/4\epsilon_0 bc]

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