Electric Field
The Physics Hypertextbook™
© 1998-2008 by Glenn Elert -- A Work in Progress
All Rights Reserved -- Fair Use Encouraged
Discussion
introduction
The electric field isn't real. It's just something some guy (Michael Faraday) made up to make it easier to think about the universe. Unfortunately, when students hear something was made up, they automatically see that something as something they have to think about and learn. They see it as something difficult. No one ever thinks about the alternatives. What if the electric field had never been invented? What would life be like without it? The answer to that is "horribly different", because the field was the gift that Michael Faraday gave to the rest of us. The field makes it easier to think about the universe. When it's easier to think about the universe, it's easier to work with the universe and use its laws to make stuff. What a horrible inconvenience for the rest of us. What a frightening world we live in, where arbitrary decisions are made, and students find themselves tormented with ideas that work. The electric field is a really important idea about something that doesn't "really" exist.
Some text and some diagrams.
| and so on … |
And more diagrams.
| and so on … |
And maybe some mathematics. In classical field theory, the strength of the field at a point is the normalized value of the field. In other words …
| field = | force |
| quantity |
For electricity, this becomes …
| E = | FE |
| q |
There is no special name for its unit, nor does it reduce to anything simpler.
| ⎡ ⎣ |
N | = | kg m/s2 | = | kg m | ⎤ ⎦ |
| C | A s | A s3 |
We will see later that this is equivalent to …
| ⎡ ⎣ |
N | = | V | ⎤ ⎦ |
| C | m |
Some values …
| Electric Field Strength (just a start) | |
| E (V/m) | location, event |
|---|---|
| 3 × 106 | dielectric breakdown of air |
| 120 | earth's surface (sea level) |
For point charges …
| E = | 1 | q | ˆr | or | E = k | q | ˆr | |
| 4πε0 | r2 | r2 |
For multiple point charges …
| E = | 1 | ∑ | dq | ˆr | or | E = k ∑ | dq | ˆr |
| 4πε0 | r2 | r2 |
For continuous charge distributions …
| E = | 1 | ⌠ ⌡ |
dq | ˆr | or | E = k | ⌠ ⌡ |
dq | ˆr |
| 4πε0 | r2 | r2 |
Summary
- bullet
Problems
practice
- sketch-e.pdf
The diagram on the accompanying pdf file shows the location and charge of two identical small spheres. Find the magnitude and direction of the electric field at the five points indicated with open circles. Use these results and symmetry to find the electric field at as many points as possible without additional calculation. Write your results on or near the points. Sketch the approximate magnitude and direction of the field at these points.- Answer it.
- Sketch the electric field around the following pairs of point charges. Draw continuous
field lines and assume the charges are separated by a few centimeters
of empty space.
- A +3 μC charge on the left and a +1 μC charge on the right.
- A +3 μC charge on the left and a −1 μC charge on the right.
- Answer it.
- Write something nice.
- Answer it.
- Write something completely different.
- Answer it.
numerical
- The electric field of the earth is due to the separation of charges
between the surface of the Earth and the upper layers of the earth's
atmosphere.
- If the direction of the earth's electric field points down, what is the sign of the charge on the earth's surface and the sign of the charge in the earth's upper atmosphere? Explain your answer.
- An estimate of the net charge on the earth can be made by assuming that all of the charge on the earth is concentrated at its center. If the electric field on the earth's surface is 120 V/m, what is the net charge of the earth?
- All of this charge is actually spread out over the surface of the
earth. Determine the average surface charge density of the earth
in …
- coulombs per square meter [C/m2] and
- elementary charges per square millimeter [e/mm2].
- Do your answers to part c represent an excess or a deficit of electrons? Explain your answer.
- A charge of -1.0 μC is located on the y-axis 1.0 m
from the origin at the coordinates (0,1) while a second charge of +1.0 μC
is located on the x-axis 1.0 m from the origin at the coordinates
(1,0). Determine the …
- magnitude and
- direction
- The drawing to the right shows two charged objects, one located at the origin indicated by a solid circle and a second located first at point A and then at point B (indicated by open circles). Points on the grid are separated by one meter. Thus point A is 3 m right and 4 m down relative to the origin and point B is 8 m right and 6 m up relative to the origin. The electrostatic force on the second charge is 20 N when it is located at point A. Determine the electrostatic force when the second charge is moved to point B.
Resources
- general
- Franklin: An Electrostatic Field Tracer for Macintosh Computers, Paul Peters
- The Mechanical Universe and Beyond (video on demand, login required)
- The Electric Field, Faraday's vision of lines of constant force in space laid the foundation for the modern force field theory.
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