Electric Field Strength

Electric Field Strength

The Electric field strength (E) at a given point is defined as the Force experienced by a unit positive charge at that point.

Where :-

E - Electric field strength (NC-1)

F - Force experienced by the charge (N)

Qt - Charge of the Charged particle (C)

As direction of the force is dependant on charge type, Electric Field Strength is a Vector quantity.

Note - The above formula is analogous to gravitational field strength (g = F/m) where g has units of Nkg-1.

By substituting the value for Force gained using Coulomb's Law, the following formula for Electric field strength can be derived :-

Therefore by substituting into the above Electric field strength formula :-

Note - The Electric field strength is inversely proportional to r 2 and if plotted as a graph, follows and exponential relationship :-

Example 1-

Two Point charges Qa and Qb are placed at points A and B, where the separation AB is 0.5m. if Qa has a charge of +2x10-6 C, calculate the total Electric field strength at the midpoint of AB if :-

Qb = +3x10-6 C

Qb = -3x10-6 C

For Qb = +3x10-6 C :-

As both charges have the same sign, the fields at the midpoint between them are in opposite directions. Therefore, the total Electric field strength at this point is the difference between them.

Note - As these are positive charges, a test (positive) charge would be repulsed by both.

Total Electric Field Strength = Eb - Ea

E = 3.6x104 NC-1

The Total Electric field strength is 1.4x105 NC-1 in the direction of B towards A.

For Qb = -3x10-6 C :-

As both charges have the opposite sign, the fields at the midpoint between them are in the same direction. Therefore, the total Electric field strength at this point is the sum of them.

Total Electric field strength = Eb + Ea

E = 1.8x105 NC-1

The Total Electric field strength is 1.8x105 NC-1 in the direction A towards B.

Example 2 - ( Electric Dipole )

A Pair of charges Q1 ( +4x10-9 C ) and Q2 ( -4x10-9 C ) are separated by 2x10-14 m and make an electric dipole.

Calculate the Electric field strength at point P, which is 5x10-14 m from the dipole as shown below :-