Determine the potential energy function of the charged particle

[SLTH02]

Homework Statement

The electrostatic force repelling a charged particle from a long, straight, uniformly charged rod is given by
the equation F = 100 x ^ (-1) where x is the distance from the rod.

Relevant Equations

F = -(dU)/(dx)

I understand that you need to integrate f(x), and the negative of that is U(x).

But the last part of the problem says "Clearly state any assumptions you make."

And the answer is just the antiderivative of that f(x) without any constant from integrationHow does that make sense

 

[BvU]

Good observation. You might insert the actual question in the homework statement, but I gather the exercise asks for 'the' potential energy function.

Such a function is in fact determined to within a constant (we don't observe potentials, only forces ...) . Usually we take the potential to be zero at infinity, but in this case that can not be done: a consequence of assuming the linear charge is itself infinitely long.

 

[SLTH02]

a consequence of assuming the linear charge is itself infinitely long.

So what would happen if the linear charge is infinitely long?

 

[BvU]

An infinitely long wire looks the same from any distance,

A better question is: what would change if the wire had finite length
(nice exercise: check that ##V\rightarrow {Q\over {4\pi\varepsilon_0 r} } ## for ##d\rightarrow \infty## )

 

[SLTH02]

An infinitely long wire looks the same from any distance,

A better question is: what would change if the wire had finite length
(nice exercise: check that ##V\rightarrow {Q\over {4\pi\varepsilon_0 r} } ## for ##d\rightarrow \infty## )

Got it. thanks!