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 ar 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. The electric field as a vector field.
|and so on…|
And more diagrams. The electric field as field lines.
|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…
For electricity, this becomes…
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…
For point charges…
|E =||1||q||r̂||or||E = k||q||r̂|
For multiple point charges…
|E =||1||∑||dq||r̂||or||E = k ∑||dq||r̂|
For continuous charge distributions…
|dq||r̂||or||E = k||⌠