Electric Current of an Orbiting Electron

[FelaKuti]

Homework Statement

The question is based on the Bohr model with an electron with charge e and mass m orbiting a proton about a circular radius r.

I have to find k in the equation I = e² / sqrt kε₀r³m

where k is a some combination of constants.

Homework Equations

Coulumb's force law: F = kq₁q₂/r²

Centripetal force: mω²r

Current: I = q/t

k = 1/4πε₀

The Attempt at a Solution

I equated columb's force law to the centripetal force to give mω²r = ke²/r²

Then rearranged to get ω² = ke²/mr³

Then I changed ω for 2π/T and square rooted both sides to give 2π/T = ke²/mr³

From here I'm just not sure how to get it into the form of the equation asked for.

 

[TSny]

ω² = ke²/mr³

2π/T = ke²/mr³

The left side of the second equation above has an error (maybe just typographical).

From here I'm just not sure how to get it into the form of the equation asked for.

Try to make use of I = q/t.