Electric Fields

Coulomb’s Law

Electric Force

Coulomb’s law states that the electric force is directly proportional to the product of the charges and inversely proportional to the squared distance between them.

Electric Fields, figure 1

__F __= Force (N)

ε0= Permittivity of free space

__Q __= Charge of one object (C)

q = Charge of second object (C)

__r __= Distance between them (m)

The permittivity of free space is a measure of how well a field permeates, or spreads throughout, a region. In this case we are going to treat the permittivity of air as being equal as that of a vacuum (free space).

Electric Field Strength

Drawing Electric Fields

Electric Fields, figure 1

Notice the direction of the field lines. They are pointing from positive and going to the negative plate.

Electric Fields, figure 2

If one source was more charged and therefore had a larger electric field, the points at which the resultant force is zero would be shifted towards the weaker charge.

Electric Fields, figure 3

Electric Field Strength

Electric Fields, figure 4

Work Done

Electric Fields, figure 5

Moving Charges

Electric Fields, figure 6

Notice that the shape of the trajectory is parabolic.

Electric Field Strength 2

The magnitude of the electric field strength is similar to that of the gravitational field in design;

Electric Fields, figure 7

Electric Potential

Electric potential works the same as gravitational potential. It is the work done when moving an object from infinity to a point in the field.

Similarly electric potential difference is the work done in moving a charge from one point to another point in an electric field.

Work Done

Work done: Electric Fields, figure 1

Yes - this is similar to gravitational work done.

Equipotential Surfaces

Electric Fields, figure 2Electric Fields, figure 3

The dotted green lines are the lines of equipotential.

Electric Potential and Electric Field Strength

Electric potential and electric field strength are related by the following relation:

Electric Fields, figure 4