Electric Fields

In physics, an electric field is a property that describes the space that surrounds electrically charged particles or that which is in the presence of a time-varying magnetic field. This electric field exerts a force on other electrically charged objects. The concept of an electric field was introduced by Michael Faraday.

Precise measurements of electrical charge were carried out by the French physicist Charles Coulomb in the 1780's using a device called a torsional balance measuring the force

generated between two electrically charged objects. The results of Coulomb's work led to the development of a unit of electrical charge named in his honor, the coulomb. If two "point" objects (hypothetical objects having no appreciable surface area) were equally charged to a measure of 1 coulomb, and placed 1 meter (approximately 1 yard) apart, they would generate a force of about 9 billion newtons, either attracting or repelling depending on the types of charges involved.

The operational definition of a coulomb as the unit of electrical charge (in terms of force generated between point charges) was found to be equal to an excess or deficiency of about 6,250,000,000,000,000,000 electrons. Or, stated in reverse terms, one electron has a charge of about 0.00000000000000000016 coulombs.

Being that one electron is the smallest known carrier of electric charge, this last figure of charge for the electron is defined as the elementary charge.

1. Force between charges

Coulomb’s law

an example of an inverse square law.

Forces between collinear charges.

Draw the diagram of the particles and the charges on these particles.

Use the formula to calculate the force between charges.

Draw this force upon each particle, include the direction that the force is acting in. When you have worked out the forces between all the charges, combine the forces (adding if the are going the same direction and subtracting if in opposite directions)

Appropriate calculations.

Ex 19.1 Real World Physics

2. Electric fields

The strength of the field at a given point is defined as the force that would be exerted on a positive test charge of +1 Coulomb placed at that point;

the direction of the field is given by the direction of that force.

Electric fields contain electrical energy with energy density proportional to the square of the field amplitude.

The electric field is to charge as

gravitational acceleration is to mass

and density is to volume.

An electric field that changes with time (such as due to the motion of charged particles in the field) will also influence the magnetic field of that region of space. Thus, in general, the electric and magnetic fields are not completely separate phenomena; what one observer perceives as an electric field, another observer in a different frame of reference perceives as a mixture of electric and magnetic fields. For this reason, one speaks of "electromagnetism" or "electromagnetic fields." In quantum mechanics, disturbances in the electromagnetic fields are called photons, and the energy of photons is quantized.

from Wilkipedia


*An Electric Field is a region is space where an electric charge at rest experiences a force other than the force of gravity.

Not strictly true; a proton at rest could experience a ‘strong’ nuclear force, but we will conveniently ignore that for now.

An Experiment from


The apparatus of the experiment consisted of a glass tray with a small layer of tap water that had two fixed electrodes sitting inside of it that were hooked up to a power supply in order to create an electric field within the tap water. Under the glass tray was a coordinate system that allowed the plotting of data points as the varying voltages were obtained. The voltage was read using a voltmeter connected to a freely moving probe to collect the necessary data. In the first part of the experiment, the voltage readings were used to collect data for 1.0 volts, 2.0 volts, etc while the position of each reading was recorded on graph paper

Idea of lines of force.

Like in magnetism, these lines join places of equal electric strength

Lines go from +ive to -ive

Note that where the electric field is strong, the field lines are close together; where the field is weak the lines are far apart

Vector nature of electric field to be stressed.

That opposite charge attract and that like charges repel, therefore we can see that the directions of force depends on the type of charges

Demonstration of field patterns using oil and semolina or other method.

Connect the High V supply to some thin point conductors in a petri dish

Definition of electric field strength.

* Electric Field Strength’ aka Electric Field Intensity

Why have a concept called ‘Electric Field Strength’?

Because we may need to know what effect a given charge would have on another charge, if that second charge was placed a certain distance from it.

But you can’t say that the first charge would produce a force of say 10 Newtons. Why not?

Because the size of the force depends on the magnitude of the two charges.

So to get around this we need a nominal second charge, and it makes sense to nominate this second charge to be unit charge, i.e. one Coulomb.

This means that if we know the effect the first charge will have on a charge of one Coulomb, we can get a feel for how strong it is.

This is important when designing circuit boards for example.

E = electric field strength (NC-1)

F = force

q = charge (C)

What was Electrostatic Force ??

So divide by q

as you can see the formula for Electric field strength is almost the same as the Force formula, the only thing it is short is the other charge value.

Thus the units of electric field are related to the unit of Force the Newton divided by the unit of Charge the Coulomb, NC-1 or N/C

The electric field is a vector field with SI units of

  1. Newtons per Coulomb (NC−1)The SI base units of the electric field are kg·m·s−3·A−1 or,
  2. Volts per metre (Vm−1).

Appropriate calculations. collinear only

Real World Physics exercise 19.2

Applications of Electric Fields.


The first use of corona discharge to remove particles from an aerosol was by Hohlfeld in 1824. However, it was not commercialized until almost a century later. In 1907 Dr. Frederick G. Cottrell applied for a patent on a device for charging particles and then collecting them through electrostatic attraction — the first electrostatic precipitator. He was then a professor of chemistry at the University of California, Berkeley. Cottrell first applied the device to the collection of sulfuric acid mist and lead oxide fume emitted from various acid-making and smelting activities. Vineyards in northern California were being adversely affected by the lead emissions.At the time of Cottrell's invention, the theoretical basis for operation was not understood. The operational theory was developed later in the 1920s, in Germany.


Explosion in flour-mills

Explosion when fuelling

Damage to integrated circuits.

Electric shock

3. Potential difference

we first met the idea of potential in mechanics, it is considered to be energy due to position .....

in electricity we also have this idea. Where a charge might be out of place due to another attraction

Concept of zero potential.

We talked previously that the earth is the source and sink of all charge..... therefore the net charge on earth = 0V

Scalar value ? or ?

Definition of potential difference:

work done per unit charge to transfer a charge from one point to another.

Work = Charge x Potential Difference

Definition of volt

of course work is energy

and so V is measured in JC-1 or J/C

1 V = 1 JC-1 or 1 J/C


Appropriate calculations.

Real World Physics pg 237 ex 20.1


i W = qV = 400, W = Fxd => F = W/d = 400/0.02 = 20,000

ii E = F/q = 20,000

iii F = E x q = 20000 x 1.6 *10-31 =

iv potential energy lost = Work done .... W = QV

v = W = 1/2mv2 =