MHB Answer: Calculate Electric Field Strength at 1mm for a Stationary Electron

[Alexis Deleon]

Question: A stationary electron is a point of charge. What is the energy density of U, it's electric field at a radial distance r=1mm?

Know:
1mm=1*10^-3m
u=(1/2)(epsilon naught)(E^2)
E=kq/r^2

I know I have to end up solving for (E)^2, where E=kq/r^2, but how do I determine what charge to use for q?

 

[I like Serena]

Question: A stationary electron is a point of charge. What is the energy density of U, it's electric field at a radial distance r=1mm?

Know:
1mm=1*10^-3m
u=(1/2)(epsilon naught)(E^2)
E=kq/r^2

I know I have to end up solving for (E)^2, where E=kq/r^2, but how do I determine what charge to use for q?

Welcome to MHB Alexis Deleon! :)

The charge q is the negative elementary charge, usually denoted with the symbol $\text{e}$, which is also the first letter of the word electron:
$$q = -1 \text{ e} = -1.602 \cdot 10^{-19} C$$

Note also that:
$$k = \frac{1}{4\pi \epsilon_0}$$

So:
$$U=\frac 1 2 \epsilon_0 E^2
= \frac 1 2 \epsilon_0 \left( \frac {kq}{r^2}\right)^2
= \frac 1 2 \epsilon_0 \left( \frac{1}{4\pi \epsilon_0} \frac {-1\text{ e}}{r^2}\right)^2$$