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In physics, an electric field is an effect produced by an
electric charge that exerts a force on objects in its vicinity.
Definition and derivation
The mathematical definition of the electric field is developed
as follows. Coulomb's Law gives the force between two point charges
(infinitesimally small charged objects) as
- , where
- ε0 (pronounced epsilon-nought) is a physical constant, the permittivity of free space;
- q1 and q2 are the electric charges of the
objects;
- r is the magnitude of the separation vector between the objects;
- is the unit vector representing the direction from one charge to the other.
In the SI system of units, force is given in newtons, charge in coulombs, and distance in meters. Thus, ε0 has units of C²/Nm².
This was known empirically. Suppose one of the charges is taken to be fixed, and the other one to be a moveable "test charge".
Note that according to this equation, the force on the test object is proportional to its charge. The electric field is defined
as the proportionality constant between charge and force:
-
- (1)
Properties
According to Equation (1) above, electric field is dependent on position. The electric field due to any single charge
dissipates as the square of the distance from that charge.
Electric fields follow the superposition principle. If more than one charge is present, the total electric field at any point
is equal to the vector sum of the respective electric fields that each object
would create in the absence of the others.
-
If this principle is extended to an infinite number of infinitesimally small elements of charge, the following formula
results:
-
where ρ is the charge
density, or the amount of charge per unit volume.
The electric field can also be thought of as the gradient of the electric potential. If several spatially distributed charges generate
such an electric potential, e.g. in a solid, an electric field gradient
may be defined.
Related topics
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