Question 16.5: ELECTRIC POTENTIAL ENERGY AND DYNAMICS GOAL Apply conservati...
ELECTRIC POTENTIAL ENERGY AND DYNAMICS
GOAL Apply conservation of energy and electrical potential energy to a configuration of charges.
PROBLEM Suppose three protons lie on the x-axis, at rest relative to one another at a given instant of time, as in Figure 16.9. If proton q_{3} on the right is released while the others are held fixed in place, find a symbolic expression for the proton’s speed at infinity and evaluate this speed when r_{0}=2.00 \mathrm{fm}. (Note: 1 \mathrm{fm}=10^{-15} \mathrm{~m}.)
STRATEGY First calculate the initial electric potential energy associated with the system of three particles. There will be three terms, one for each interacting pair. Then calculate the final electric potential energy associated with the system when the proton on the right is arbitrarily far away. Because the electric potential energy falls off as 1 / r, two of the terms will vanish. Using conser vation of energy then yields the speed of the particle in question.
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