Question

Assume that a stationary electron is a point of charge. What is the energy density u of its electric field at radial distances

(a) r = 9.30 mm, (

b) r = 9.30 μm,

(c) r = 9.30 nm, and

(d) r = 9.30 pm?

(e) What is u in the limit as r right-arrow 0 (u right-arrow 0 = 1, u right-arrow infinity = 2)?

Answer 1

here,

charge of electron , q = 1.6 * 10^-19 C

(a)

r = 9.3 mm

r = 9.3 * 10^-3 m

electric feild , E = K*q/r^2

energy density , u = 0.5 * epsilon0 * E

u = 0.5 * 8.85 * 10^-12 * 9 * 10^9 * 1.6 * 10^-19 /( 9.3 * 10^-3)^2

u = 7.37 * 10^-17 J/m^3

the energy density is 7.37 * 10^-17 J/m^3

(b)

r = 9.3 um

r = 9.3 * 10^-6 m

electric feild , E = K*q/r^2

energy density , u = 0.5 * epsilon0 * E

u = 0.5 * 8.85 * 10^-12 * 9 * 10^9 * 1.6 * 10^-19 /( 9.3 * 10^-6)^2

u = 7.37 * 10^-11 J/m^3

the energy density is 7.37 * 10^-11 J/m^3

(c)

r = 9.3 nm

r = 9.3 * 10^-9 m

electric feild , E = K*q/r^2

energy density , u = 0.5 * epsilon0 * E

u = 0.5 * 8.85 * 10^-12 * 9 * 10^9 * 1.6 * 10^-19 /( 9.3 * 10^-9)^2

u = 7.37 * 10^-5 J/m^3

the energy density is 7.37 * 10^-5 J/m^3

(d)

r = 9.3 pm

r = 9.3 * 10^-12 m

electric feild , E = K*q/r^2

energy density , u = 0.5 * epsilon0 * E

u = 0.5 * 8.85 * 10^-12 * 9 * 10^9 * 1.6 * 10^-19 /( 9.3 * 10^-12)^2

u = 73.7 J/m^3

the energy density is 73.7 J/m^3