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 Q_{1} and Q_{2} 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
