Electric fields

To recall, Coulomb's Law KBhPHYS201ColoumbsLaw looks like \(F_{attraction} = k\frac{Q_1Q_2}{R^2}\), which is eerily similar to the Force of Gravity, \(F_{grav} = G\frac{M_2M_2}{R^2}\).

And so, by the some token, we could also redefine electric force by splitting the function in the same way as with gravity fields:

\definition{Electric Field}{\(E = \frac{k \times Q_2}{R^2}\)} \definition[where $E$ is $Q_2$'s electric field]{Electric Force}{\(F_{attraction} = E Q_1\)} Unsurprisingly, the units for Electric Field is \(\frac{N}{C}\), and no, before you get excited, there is nothing it equals.

With masses (and w.r.t. KBh_{PHYS201GravitationalFields} gravitational fields), it's easy. Masses always attracts because negative mass doesn't exist (yet). But, with an electric field, figuring out directions is harder.

So, we have two choices to dealing with directions:

1. Electric field of any \(Q\) has two values, one "attract field" and one "repel field"
2. Drawing a single vector \(\vec{E}\), but remember that the direction of the vector depends on what's dropped in it

USE OPTION 2.

In this manner, when we say, "this atom has a electric field vector in this direction", we mean two things

1. When a positive test change is dropped onto that vector, it will experience force in the same direction as the vector
2. When a negative “” “” “","” “” “” the opposite direction as the vector

There are two ways of illustrating electric fields — either drawing an infinite amount of vectors (that's a lot of vectors), or drawing lines originating from the main particle lining up all the vectors (Think! The original Japanese flag.)

See KBhPHYS201IllustratingElectricFields illustrating electric fields.

See KBhPHYS201ElectricFieldInteractions Electric Field Interactions.

To get our modern world, Conductors — metals and other elements in which electrons could move freely — are an important item to study and model. Lots of problems involve interactions between electrons + electric fields being placed in and around conductors.

See KBhPHYS201ConductorsEquilibrium

In addition to the measurements of field strength with \(\frac{N}{C}\), there is a unit called Volts (\(V\)), measuring the amount of energy in an electric field.

See KBhPHYS201Voltage

Take, a neutral conductor.

Screen Shot 2020-08-24 at 9.44.46 PM.png

At the point of the cursor, there would be an electric field cause by the central charge going outwards; at which point the following will happen…

1. The red (positive) charge attracts electrons to the inside of the tube
2. These newly electrons set up their own electric fields equal and opposite to the electric field by the central electron (because of the Electric Field Deux. Gravitational Field thing)

So, the conductor has a net electric field of 0. It's static.

Because of the fact that the neutral conductor had both 1) and 2) going on, there is no tangent changes to the conductor (think! rule 2 aforementioned), and only field lines that are perpendicular (emitted by the red, positive charge), will be passed out.

KBe20phys201refVoltage

Annotated document: SRCelectrostaticsPacket1annotatedExr0n.pdf