## Thursday, February 20, 2020

### Unizor - Physics4Teens - Electromagnetism - Electric Field - Voltage

Notes to a video lecture on http://www.unizor.com

Voltage

Recall the concept of the electric field potential.
By definition, the electric field potential is a quantitative characteristic of an electric field, defined for each position in this field, as the amount of work needed to move a probe - positively electrically charged point-object of +1C (one coulomb) - from infinitely remote point in space, where the field does not exist, to this position in the field.

Also recall that in an electric field amount of work to move a charge from one position to another is independent of a trajectory because electrostatic forces are conservative. So, amount of work to move a charge from point A to point B along a straight line between them is the same as if we move along some curve or go from A to an infinitely far point and then return to B.

Electric potential for each point of an electric field fully defines this field. If we know the electric potential at each point of a field, we don't have to know what kind of an object is the source of the field, nor its charge, nor shape in order to understand the movement of any probe object in this field.

To find the amount of work needed to move a charge q from a point in the electric field with a potential V1 to a point with potential V2 we can simply multiply the electric charge by the difference of electric potentials between these points:
W = q·(V2−V1)
The sign of the resulting value of work W is important. It signifies whether outside force has to perform the work against the forces of the electric field (like forcing a positive charge to go further from the attracting negative charge) or the electric field does the work itself (like forcing a positive charge to go further from the repelling positive charge).

The expression in the parenthesis in the above formula for work W, that signifies the difference in electric potentials between two points in the electric field, is the main component to calculate the work needed to move a charge between these points. This expression has a special name - voltage - in honor of Italian physicist Alessandro Volta.

Since the electric potential is the work performed on the unit charge, the convenient unit of measurement of this potential is the unit of work per unit of charge.

This unit of measurement is called volt (symbol V) and it is defined as such a difference in electric potential between two points in an electric field that one joule of work (1J) is required to move one coulomb of positive charge (+1C) between these points:
1V = 1J/1C

In the electric field produced by an electrically charged point-object with Q amount of electricity the potential at any point depends only on its distance R from the source of the field and equals to k·Q/R. So, the voltage between two points at distances R1 and R2 equals to
ΔV = k·Q·(1/R1 − 1/R2)

In the electric field produced by an electrically charged infinite plane with density of charge σ the intensity of the field is constant for all points in space and is equal to 2π·k·σ (see Problems 2 of this section). The direction of the force is always perpendicular to the plane. Therefore, moving a probe charge parallel to the plane does not require any work, and the only parameter we have to take into consideration is the height above the plane. The amount of work needed to move a probe charge of +1C from the height H1 to height H2 is the product of the force (intensity of the field) by distance (difference in height). Therefore, it equals to
ΔV = 2π·k·σ·(H2−H1)

Important Analogy

Producing electric charge by separation of electrons from the neutral atoms can be compared with raising the level of water (or any other liquid) in the tall vertical tube with closed valve at the bottom in the gravitational field of Earth.
Electric charge causes the existence of electric field that is the source of a force on any electrically charged object.
The water raised to a certain height is the source of pressure, which is the force acting on any object at the bottom.
The voltage, which is a difference in electric potential between two points in the electric field is analogous to a difference in potential energy between the water at two different heights.
Connecting positive and negative charges will cause their mutual neutralization, so no electric field and no voltage will be present anymore.
Opening a valve in the vertical tube with water will cause the water to flow down, and no pressure will exist anymore at the bottom of the tube.

This analogy might be useful to understand many facts related to electricity, and it goes much deeper than just about voltage. Electric generators, electric motors, conductors, resistors etc. - all can be to an extent compared with corresponding water-based devices. We will address these concepts, as we progress with the course.