Electrostatics

1/3 in AP Physics C: Electricity & Magnetism. See all.

Warning

These notes are as I originally wrote them with minor edits for readability. This means that you may see phrases like “charges be frickin chargemental” without explanation.

charges be frickin chargemental

Can be positive or negative (though these words technically have no meaning — a “positive” charge could equally be called a “red” charge. We only say positive and negative as convention so that our computations are easier).
is the elementary charge (the smallest charge ever measured on an isolated particle — protons have a charge of and electrons have a charge of ). This means that charge is not a continuous function! Charge can only be in increments of

A “” is not just a terrible grade — it’s also a Coloumb, the unit of charge! Since Coloumbs are a LOT, you’ll need to know these (though they’re given on the formula sheet): µC (micro) is one millionth, nC (nano) is one billionth, and pC (pico) is one trillionth of a Coulomb.

Coulomb’s Force/Electrostatic Force/Electric Force ()
This is pretty much what all of E&M boils down to. The equation for this force (I’m assuming you’ve taken Mechanics; if you don’t know what forces are, this might not be the class for you yet) is:

where

Coulomb’s constant (on the formula sheet btw)
the charge on each object
the distance between the centers of charge of the two objects. Sometimes the radius (if the two objects are touching and the radius of one is negligible compared to the other type shit).
Look familiar? It’s similar to Newton’s universal gravitational force equation.

Charging by Friction
Rubbing two objects together tends to cause one of them to lose electrons and the other to gain electrons (e.g. if you rub a balloon with fur, the balloon becomes negatively charged).

Charging by Conduction
The two objects have to touch, and both end with the same sign of net charge.

induction is opposite

Electric Field
The ratio of the electrostatic force to the charge of the positive test charge. A test charge is a charge small enough to not measurably change the electric field it is placed in.

where (explain).

not all charges are point charges! sometimes we have…

Continuous Charge Distributions
Basically, “charge with shape”.

Electric Potential Energy

or, at a certain point,

Electric Potential
Is essentially the electric potential energy per unit of charge placed in a certain point. Essentially, it’s the electric potential energy of a test charge at a certain point.

Electric potential is a scalar attribute of a vector electric field (remember, energy doesn’t have a direction!). Mostly, we work with the change in potential between two points, or electric potential difference, represented by instead of just electric potential. So,

It’s convention to set the electric potential at point to which means that the electric potential difference between and is just the electric potential of We can also show that .

Work to Move a Charge
Man would I love a job right about now. Anyways. The work to move a charge from to is

because, as we know from Mechanics, which is the electric potential difference times the charge (or, the change in electric potential energy).

Electron Volt
An electron volt is defined as the energy a charge-field system gains or loses when a charge of magnitude is moved through an electric potential difference of (remember that ).

Surface Charge Density
Charge per unit area, given by

Electric Flux
Flux is defined as any effect that appears to pass or travel through a surface or substance. Flux is denoted by the uppercase Greek letter phi: Electric flux, creatively, is flux with a capital-E subscript: It’s defined as the amount of electric field that passes through a defined area. Since it’s the measure of field-by-area, which is easy to remember because it’s acronym of Electronic Arts (and it’s on the formula sheet… 😊). The “direction” of area is always perpendicular to the surface and, for closed objects, faces outwards.

Permittivity of Free Space
Describes the ability of a vacuum to permit electric fields

Guass’s Law

cylinder to find the electric field of one infinite plane gives you Take two parallel, infinite planes and the field outside of the two planes will equal while the field inside will be So, the electric field between two parallel plates is equal to (surface charge density).

Conductors are materials where charges are free to move rather easily. A special case of this is conductors in electrostatic equilibrium (i.e. conducting objects with no moving charges). There are four properties that you need to know for such conductors:

The electric field inside the object is zero (you can prove why this must be true!).
All excess charges (if any) are located on the surface of the conductor.
The electric field at the surface of the conductor is perpendicular to the surface and is equal to the local surface charge density divided by the permittivity of free space.
For an irregular shape, when the radius of curvature is at its minimum. That is, the curviest part of the shape will have the most excess charge per unit area.

Item #1 also leads to a phenomenon called Electrostatic Shielding, which is essentially that anything inside of a conductor in electrostatic equilibrium is shielded from any external electric fields.

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