Charge q1 is distance r from a positive point charge q. charge q2=q1/3 is distance 2r from q. what is the ratio u1/u2 of their potential energies due to their interactions with q?

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19-02-2017
Physics

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Charge q1 is distance r from a positive point charge q. charge q2=q1/3 is distance 2r from q. what is the ratio u1/u2 of their potential energies due to their interactions with q?

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Аноним Аноним · Answer 1 · 2017-02-24T11:28:27+01:00

We need the power law for the change in potential energy (due to the Coulomb force) in bringing a charge q from infinity to distance r from charge Q. We are only interested in the ratio U₁/U₂, so I'm not going to bother with constants (like the permittivity of space).

The potential energy of charge q is proportional to
∫[s=r to ∞] qQs⁻²ds = -qQs⁻¹|[s=r to ∞] = qQr⁻¹,

so if r₂ = 3r₁ and q₂ = q₁/4, then
U₁/U₂ = q₁Qr₂/(r₁q₂Q) = (q₁/q₂)(r₂/r₁)
= 4•3 = 12.