Triangular flux

Electricity and Magnetism Level 3

A point charge q q is located at the center of a hollow icosahedron. If the flux through one face can be expressed as ( a b ) q / ϵ 0 (\frac{a}{b})q/\epsilon_0 where a a and b b are coprime positive integers , what is a + b a+b ?

Clarification: ϵ 0 \epsilon_0 is the permittivity of free space.


The answer is 21.

Geoff Pilling by Geoff Pilling , 53, USA

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1 solution

Geoff Pilling
Jun 28, 2016

The total flux is q / ϵ 0 q/\epsilon_0 . By symmetry 1 / 20 t h 1/20th goes through each of the icosahedron's 20 20 faces. So the flux though one face is ( 1 / 20 ) q / ϵ 0 (1/20)q/\epsilon_0 . 1 + 20 = 21 1+20 = \boxed{21}

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