electric potential problem A decade before Einstein published his theory of rela
ID: 1399067 • Letter: E
Question
electric potential problem
A decade before Einstein published his theory of relativity, J.J. Thomson proposed that the electron might consist of small parts and attributed its mass to the electrical interaction of the parts. Furthermore, he suggested that the energy equals mc^2 . Make a rough estimate of the electron mass in the following way: assume that the electron is composed of three identical parts that are brought in from infinity and placed at the vertices of an equilateral triangle having sides equal to the classical radius of the electron, 2.82 x 10^-15 m.
(a) Find the total electric potential energy of this arrangement.
(b) Divide by c^2 and compare your result to the accepted electron mass (9.11 x 10^-31 kg). (The result improves if more parts are assumed.)
Explanation / Answer
a) potentail energy of the system of 3 charges, E = 3*k*q^2/r
= 3*9*10^9*(-1.6*10^-19/3)^2/(2.82*10^-15)
= 2.723*10^-14 J
b) mass of electron, m = E/c^2
= 2.723*10^-14/(3*10^8)^2
= 3.02*10^-31 kg
this is close to 9.11*10^-31 kg
beacuse both are in the order of 10^-31
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