Electric Field   full version

SI units & Physics constants

Electricity is the branch of physics, which investigates interactions between electric charges

Here (all units see here):

 is electric force on charge q from Q

 is electric force on charge Q from q

 is position vector of charge q with respect to Q

 is electric field produced by charge Q near q

General formulas

Point charge is a charge which dimensions are small with respect to distance between the charge and the point where the electric field from this charge is defined

The electric force vector between two point charges is defined by Coulomb’s law

where  is permittivity of vacuum

Another form of Coulomb's law

where  is Coulomb constant

The magnitude of electric force

or

Electric Charges

The electric charge of object is a scalar value given by

where:

e is elementary charge

N_p and N_e are numbers of protons and electrons in the object

Charge Conservation Law

The Charge Conservation Law states that in any isolated system the net charge remains constant

where n is total number of charges in the system

The electric field

The electric field vector is defined by

The magnitude of electric field

The electric field produced by point charge Q at a distance  from the charge

Magnitude of electric field

Here P is a point where the electric field is defined

Electric field lines

Any electric field can be defined graphically by means of the electric field lines, as shown below

The electric field lines are drawn as curves so that the tangent line to the curve at arbitrary point P is directed along the vector of the electric field at this point, and the density of lines is directly proportional to the magnitude of the electric field

where:

N is the number of lines crossing a small area A, oriented normally to the electric field with the center at the point P

s is scale coefficient, which is the same for all points

The electric field lines from point charge

where  is area of sphere with radius r  and center at the charge Q

Uniform electric field

The uniform electric field is electric field where the vector  is constant everywhere in magnitude and direction

Superposition Principle

The Superposition Principle states that net electric field produced at any point by a system of charges is equal to the vector sum of all individual fields, produced by each charge at this point

where n is total number of charges in the system

The Superposition Principle for two point charges

where  and  are position vectors of point P with respect to the charges Q₁ and Q₂ respectively

The Superposition Principle for system of n point charges

where  is position vector of point P with respect to the charge  for i = 1, 2, 3,..., n

The Superposition Principle for charge continuously distributed over an object

where:

 is radius position of point where the electric field is defined with respect to small volume dV with volume charge density

V is volume of the charged object

Electric field produced by uniformly charged ring at its axis

with magnitude

where:

is radius position of point P where the electric field is defined with respect to center of the ring

R is radius of ring

Q is total charge of the ring