Electricity and Magnetism

Electric Forces and Electric Fields


In addition to mass, a particle or an object has another fundamental property that is called charge.

A charged particle has the ability to interact with other charged particles through what we call the electromagnetic interactions. The concept of charge is introduced to describe such interactions.

A particle carrying no charge is called neutral. A neutron is an example of a neutral particle.

Charge is a number and is conserved.

A proton has a charge of e = 1.6021773310-19 C. An electron has a charge of -e.

Since matter is made up of protons, neutrons, and electron, we can write the charge carried by any object as

q = Npe - Nee = (Np - Ne)e


Electrostatic interaction and electric field

Like charges repel one another and unlike charges attract one another.

Quantitative description of the interactions between charges is best carried out using the concept of electric field.

A charge creates an electric field, and an electric field acts on a charge.

An electric field is a vector field. In other words, it is an entity which has a value and a direction at every point in space.

The magnitude of the electric field E due to a point charge q is given by

E = k|q|/r2

where k = 8.9875109 Nm2/C2 is called the Coulomb constant. The direction of the electric field points away from q if q is positive and points towards q if q is negative.

Having an electric field at a point in space implys that if there is a (tiny) charge at that point, it would experience a force which has a magnitude given by

F = qE

The direction of the force F is the same as the direction of E if q is positive and is opposite to the direction of E is q is negative.

Interaction between two point charges q1 and q2

q1 creates an electric field

E = k|q1|/r2

at the position of q2. The magnitude of the force on q2 is equal to

F = q2 E = k|q1||q2|/r2

The force is attractive if the charges are of opposite sign and repulsive if they are of the same sign. The force on q1 is deduced the same way and is equal in magnitude and opposite in direction to the force on q2.

The result is the Coulomb's law:

The electric force between two charges q1 and q2 separated by a distance r has a magnitude

F = k|q1||q2|/r2

It is attractive if the charges are of opposite sign and repulsive if they are of the same sign.

Example 15.1 The electric force and the gravitational force

Superposition principle

The result of the electric field and the electric force due to a single point charge is very important because of the superposition principle.

The electric field due to multiple charges is a vector sum of the fields created by each individual charge.

The total force on a charged particle due to multiple charges is a vector sum of forces due to each individual charge.

Example 15.2 Where is the resultant force zero?

Review vector summation:

V = V1 + V2 +

Vx = V1x + V2x +

Vy = V1y + V2y +

Example 15.5 Electric field due to two point charges

Electric field lines

Pictorial representation of electric fields:

Conductors and Insulators


Materials that are made up of atoms or molecules with open shells are usually conductors.

Materials that are made up of atoms or molecules with all shells closed are usually insulators.


Conductor in electrostatic equilibrium

The charge distribution in a conductor has to be such that

simply because electric charges are free to move in an conductor. The particular nature of the electric interaction (the Coulomb's law) is such that this can only accomplished by having all the charges on the surface.

Lightning rod: The field is strongest at the sharp points.

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Copyright 1997 by Bo Gao. All rights reserved.