Practice portal › Electric Charge and Properties › Electric Charge and Coulomb's Law
Asked in GSEB Board March 2022 · Units and dimensions
Given: (Ke²)/(Gmₑmₚ), with K=1/(4πε₀) and mₑ, mₚ the electron and proton masses.
Idea: divide the top and the bottom by the same r² and the expression becomes (Ke²/r²)/(Gmₑmₚ/r²) -- the electrostatic force between an electron and a proton divided by the gravitational force between them at the same separation.
A ratio of two quantities of the same kind is a pure number.
Check it in full: [K]=M¹L³T⁻⁴A⁻² and [e²]=T²A², so the numerator is M¹L³T⁻².
[G]=M⁻¹L³T⁻² and [mₑmₚ]=M², so the denominator is M¹L³T⁻² as well.
The two are identical, so the dimensions are M⁰L⁰T⁰A⁰. Its value, about 2×10³⁹, is how many times stronger the electric attraction is than the gravitational one.
Reading this solution needs no sign-in. You only sign in to practise against the clock and keep your progress.
Practise this with a timer