# Electrostatics

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• Last Post 29 April 2018
Chris posted this 28 April 2018

The definition of Electrostatics is the following:

Static electricity is an imbalance of electric charges within or on the surface of a material. The charge remains until it is able to move away by means of an electric current or electrical discharge. Static electricity is named in contrast with current electricity, which flows through wires or other conductors and transmits energy.

Electrostatics was at the inception of our knowledge of Electricity.

So, what is Electrostatics?

I have always been a Richard Feynman fan: The Feynman Lectures on Physics - Electrostatics, a lot of good information exists in the texts! A lot of our important Laws have come to pass, including Coulombs Law, Amperes Law and so on.

Onepower has kindly shared some good resources also:

http://amasci.com/miscon/whatis.html

http://amasci.com/miscon/voltage.html

http://amasci.com/emotor/voltmeas.html

Richard Feynman starts his physics lectures on Electrostatics of stating: [Topic: Maxwell's Equations]

The situations that are described by these equations can be very complicated. We will consider first relatively simple situations, and learn how to handle them before we take up more complicated ones. The easiest circumstance to treat is one in which nothing depends on the time—called the static case. All charges are permanently fixed in space, or if they do move, they move as a steady flow in a circuit (so ρ and j are constant in time). In these circumstances, all of the terms in the Maxwell equations which are time derivatives of the field are zero.

We must at this stage, review the definition of the Point Charge:

a point in space that has an electrical charge that exists only in theory and that cannot be measured

The Point Charge is crutial in Coulombs Law:

Coulomb's law states that: The magnitude of the electrostatic force of attraction or repulsion between two point charges is directly proportional to the product of the magnitudes of charges and inversely proportional to the square of the distance between them.

An important Law, Coulombs Law, uses a Point Charge that by definition can not be measured, a theoretical Charge.

Already we see, problems with Electrostatics! It is a field of Science that because of our need to simplify the Dynamic, we turned to Static, however in doing so, we lost part of the Science and ended up with problems.

In Electrostatics, because we have no motion, the Point Charge is stationary in Space, thus no Current, we have no Magnetic Field, and Science tells us that Curl vanishes! Another problem we see, not because of  our lack of observation, but because of our decision to eliminate some fundamental concepts.

So how is it that Coulombs Law is important when we are missing so much? Richard Feynman on Seeking new Laws:

Again, what is Electrostatics?

It is Voltage, the Potential Difference of Charge, not Current, it is specifically Voltage.

The requirement for Voltage, is Charge Separation, Positive and Negative Charges must always be Separated. The same is true all through Science, and is not bound to Electrostatics by any means!

As Marathonman pointed out, I am still learning, and always will, for Nature is my teacher and Nature is very much smarter than I could ever be!

Chris

Chris posted this 29 April 2018

An example is always useful.

Take a Capacitor, or a Leyden Jar, either one.

Now, to be able to Charge the chosen Charge Capacity, a Separation of Charges is required. The Separation of Charges is a Voltage Potential.

We apply our Potential Difference of Charges across the Terminals of the chosen Charge Capacity - Now what happens?

The Charge Flows, or distributes itself evenly across the plates of the Charge Capacity. We use Coulombs Law to define this Capacity of now static Charge:

### Q = C · V

Where:

• Electrical Charge ( Q ) ( Coulombs ) of electrons.
• Capacitance ( C ) ( Farads ).
• Voltage ( V ) ( Volts )

Once the Capacitor has been charged, a snap shot is taken, we have static Charges on the Plates! Nothing is moving!

∇ · E = ρ / e0

∇ X E = δB / δt

e2∇ X B = δE / δt + j / e0

∇ · B = 0

The situations that are described by these equations can be very complicated. We will consider first relatively simple situations, and learn how to handle them before we take up more complicated ones. The easiest circumstance to treat is one in which nothing depends on the time—called the static case. All charges are permanently fixed in space, or if they do move, they move as a steady flow in a circuit (so ρ and j are constant in time). In these circumstances, all of the terms in the Maxwell equations which are time derivatives of the field are zero. In this case, the Maxwell equations become:

Electrostatics:

∇ · E = ρ / e0

∇ · E = 0

Magnetostatics:

∇ X B = δE / δt + j / e0c2

∇ · B = 0

You will notice an interesting thing about this set of four equations. It can be separated into two pairs. The electric field E appears only in the first two, and the magnetic field B appears only in the second two. The two fields are not interconnected. This means that electricity and magnetism are distinct phenomena so long as charges and currents are static. The interdependence of E and B does not appear until there are changes in charges or currents, as when a condensor is charged, or a magnet moved. Only when there are sufficiently rapid changes, so that the time derivatives in Maxwell’s equations become significant, will E and B depend on each other.

Now, notice the missing Time derivatives! Important to note! We are not looking at anything at all but the Static, the snapshot taken in time, which means nothing is Moving, nothing before or after this snapshot is moving in time!

We have lost all process before and after the Snapshot taken!

The Inrush Current to Charge a Capacitor can be very large! Yet we have chosen to ignore this Current. In observing Electrostatics, we loose Electrodynamics!

Chris

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The great Nikola Tesla:

Ere many generations pass, our machinery will be driven by a power obtainable at any point of the universe. This idea is not novel. Men have been led to it long ago go by instinct or reason. It has been expressed in many ways, and in many places, in the history of old and new. We find it in the delightful myth of Antheus, who drives power from the earth; we find it among the subtle speculations of one of your splendid mathematicians, and in many hints and statements of thinkers of the present time. Throughout space there is energy. Is this energy static or kinetic? If static, our hopes are in vain; if kinetic - and this we know it is for certain - then it is a mere question of time when men will succeed in attaching their machinery to the very wheelwork of nature.

Experiments With Alternate Currents Of High Potential And High Frequency (February 1892).