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A positive point charge is released from rest at distance r0 from a long line charge of uniform linear density. As it moves outward, how does its speed v depend on its instantaneous distance r from the line charge?

1. v proportional to sqrt(ln(r/r0))
2. v proportional to e^(r/r0)
3. v proportional to ln(r/r0)
4. v proportional to (r/r0)

Correct answer: v proportional to sqrt(ln(r/r0))

Solution

A line charge gives V proportional to -ln(r). The work done on the charge moving from r0 to r is proportional to ln(r/r0), which equals the kinetic energy (1/2)mv². Hence v² proportional to ln(r/r0), so v proportional to sqrt(ln(r/r0)).

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