Module 01

Electric Charge

Last Updated: Fri Aug 23 12:23:13 PM CDT 2024

Baseline Quiz

You should have already taken the baseline quiz for Module 1.

Did anybody have trouble?

Questions

Why do we get shocked all the time on metal objects during the winter?
Why do some clothes get “staticy” and stick to us?
Why does rubbing a balloon on our head make our hair stand up?

Answers

Charge

Demo

Charging some Styrofoam
Charging a pie pan
Charging a ping pong ball
How does this Electroscope work?
Why is paper attracted to the styrofoam and the pie pan?

Demo: Van de Graaff Generator

The Van de Graaff generator
Charging the ping-pong ball with the Van de Graaf generator.
Charging two spheres by inductions.

Demo: Van de Graaff Generator

A point of reference

How much charge is a lot? What if we had 1 coulomb of charge on the ping pong ball and 2 coulomb of charge on the Van de Graff generator. What would the force be if they were 1 meter apart?

A point of reference

So how much charge is on the ping pong ball?

Note on Spheres in Contact

We are assuming that the charge distributes uniformly over the two spheres when they are in contact. \[ \frac{Q_1}{R_1^2} = \frac{Q_2}{R_2^2} = \frac{Q_T}{R_T^2} \rightarrow Q_1 = \frac{R_1^2}{R_1^2 + R_2^2} Q_T \]

This is an approximation, its actually much more complicated… . . .

\[ Q_1 = \frac{R_1^2 R_2^2}{R_1 + R_2} V \sum_{n=1}^\infty \frac{1}{n(n - R_1/(R_1 + R_2))} \frac{Q_T}{C} \] Lekner 2012

Most text books use the fact that the electric potential is the same for both spheres to derive \[ \frac{Q_1}{R_1} = \frac{Q_2}{R_2} \rightarrow Q_1^\prime = \frac{R_1}{R_1 + R_2} Q_T \]
This is also an approximation…

Note on Spheres in Contact

Let’s look at the ratio of charge on each sphere:

Actual \[ \frac{Q_1}{Q_2} = \left(\frac{R_1}{R_2}\right)^2 \left(\frac{\pi^2}{6} \right)^{(R_2-R_1)/(R_1+R_2)} \]

Our Approximation \[ \frac{Q_1}{Q_2} = \frac{R_1^2}{R_2^2} = \left( \frac{R_1}{R_2} \right)^2 \]

Common Approximation \[ \frac{Q_1}{Q_2} = \frac{R_1}{R_2} \]

Digression

If we have some total charge \(Q_T\) that is split between two objects, the force between the two objects depends on how the charge is split. What distribution gives the largest force?

Adding spheres

What if we had 3 spheres? What would the force on one of the spheres be?

The Hydrogen Atom

1663 - electrostatic generator by Otto von Guericke

1785 - Coulomb’s Law confirmed

1803 - Atomic theory - John Dalton

1897 - Electron discovered - J.J. Thomson

1904 - Plum pudding model of atom - J.J. Thomson

1911 - Atomic nucleus discovered - Ernest Rutherford

1913 - Bohr model of the atom

If an atom is a positively charged nucleus surrounded by negatively charged electrons, perhaps the electrons just orbit around the nucleus like a planet around the Sun…

How fast would the electron be traveling in such an orbit?

What would the acceleration be?

Electric Dipole

The electrostatic force is very strong compared to gravity, but why don’t we feel it everywhere?
For example, it is responsible for the normal force, but that only acts over a very short distance.

Force from Electric Dipole

Force on a dipole by a dipole.

Whiteboards

What is the net force on \(q_1\)?

Last Slide

What is the net force on \(q_1\)?