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 r2 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 = 1.44x105 NC-1

The Total Electric field strength is 1.44x105 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 = 7.2x105 NC-1 

The Total Electric field strength is 7.2x105 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 2x10-14m and make an electric dipole. 

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

Conducting Shapes in Electric Fields

Any charge given to a conductor does not penetrate within the object, but is instead found only on the outer surface. This means for any charged object, the electric field (E) inside a conductor must be zero.

The field must be zero inside the conductor because if it was not zero, any charges within would be accelerated (see charges in an electric field - Higher Physics), until a balance is reached. This effective balance means there would be no overall field, as the movement of charges would create a neutral region within. 

The field outside the conductor must start perpendicular to the surface. If it did not there would be a component of the field along the surface causing charges to move until balance was reached. 

If an uncharged conductor is placed in an electric field, charges are induced as shown below so that the internal electric field strength is once again zero. 

Conducting Shapes : Faraday Cage

In the 1800s English scientist Michael Faraday discovered that an electrical conductor (like a metal cage) when charged, appeared to exhibit that charge on its surface only. It appeared to have no effect on the interior of the conductor at all. 

He set out to demonstrate this experimentally by lining a room in metal foil. He then allowed high-voltage discharges from an electrostatic generator to strike the outside of the room. 

The videos below show a full explanation of how a Faraday Cage functions, as well as an example of this in use to protect a person from high voltage discharges :-