Electric Field Revision Notes

In these revision notes for Electric Field, we cover the following key points:

• What is electric field?
• What are the similarities and differences between electric and gravitational field?
• What are electric field lines and why do we use them?
• What is the pattern and direction of electric field lines?
• What is the superposition principle of electric field?
• What are the two electric constants and which of them is more used in formulae?
• What is the pattern of electric field lines in a charged sphere?
• What is the electric field inside and outside a conducing material?
• What happens with conductors placed inside an electric field?

Electric Field Revision Notes

Electric charges are generated not only when the objects are in contact, but also when there is a certain distance between them.

Since such an interaction is quantitatively represented through the concept of electrostatic force, we can say it is a force that acts in distance, like the gravitational force. Yet, there is a similarity in the formulae of these two forces as well.

In simple words, electrostatic field is the space around a charged object in which the attractive or repulsive effect of charged objects is observed.

In the same way in which we calculate the magnitude of gravitational field strength g (i.e. by finding the weight of a 1 kg object at rest on the Earth surface, which corresponds to the gravitational force exerted by the Earth on that object), we can also calculate the magnitude of electrostatic field E. This can be achieved by considering a +1C test charge Q₀ brought near a charged object and then measuring the electrostatic force exerted by this charged object to the test charge. Thus, we can write

or

The unit of electrostatic field (for now) is [N/C]. (We will see in the next tutorial that there is another unit that is officially recognized as the unit of electrostatic field in the SI system of units).

In this way, we obtain the definition of electrostatic (or electric) field, that is

Electric field is the amount of electrostatic force exerted by a charged object on a test charge, which is at a certain distance from object.

Unlike gravitational field which has only attractive nature, electric field may have attractive or repulsive nature, depending on the charges involved.

There are no electric field lines in the shortest path between two opposite charges. It means the resultant electric field at that part of the space is zero.

We can summarize the properties of electric field lines as follows:

• Electric field lines begin at positive charges and terminate at negative ones
• The number of lines per unit area in space is proportional to the strength of electric field in that part of space
• Electric field vector at any point is tangent to the field lines passing through that point
• Electric field lines never cross or touch each other

There is another quantity, which is recognized as the "true" electrostatic constant instead of Coulomb's constant k. It is denoted by ϵ⁰ and its relation with the Coulomb's constant k is

The value of electric constant ϵ⁰ is

The constant ϵ⁰ is more common in electricity-related formulae. This is the reason why it is more important than the Coulomb's constant k.

We can therefore write for the formulae of electrostatic force and electrostatic field in terms of ϵ⁰:

and

If in a given region of space there is more than one charge that produce their own electric fields E₁, E₂, + En, the net electric field in that region is the sum of all individual electric field vectors, i.e.

The electric field produced by a charged sphere Q at a point of the space that is at distance r from the centre of the sphere, is:

When distance from centre of sphere is from 0 to R, that is for all points inside the sphere, the electric field is zero. When distance from centre is R, the electric field takes the maximum value. Then, with the increase in distance, electric field decreases until it becomes zero (at the infinity).

The electric field inside a conductor is zero. This means when we place a charge inside a cavity of a conductor, the charge does not move, as it does not experience any electric force.

This property has a wide range of applications in physics. It had been discovered by Faraday, who invented the famous Faraday's Cage, a conducting spherical grid whose internal space has zero electric field despite the grid is charged. Many electric-related phenomena have been studied by inserting the apparatuses inside such a cage, as in this way they are not affected by the surrounding electric field.