1. Electric and Magnetic Constants
In the equations describing electric and magnetic fields and their propagation, three constants are normally used. One is the speed of light c, and the other two are the electric permittivity of free space ε0 and the magnetic permeability of free space, μ0. The magnetic permeability of free space is taken to have the exact value
This contains the force unit N for Newton and the unit A is the Ampere, the unit of electric current.

2. Electric and Magnetic Constants
With the magnetic permeability established, the electric permittivity takes the value given by the relationship
where the speed of light c is given by
This gives a value of free space permittivity
which in practice is often used in the form

3. Physical Connections to Electric Permittivity and Magnetic Permeability
Expressions for the electric and magnetic fields in free space contain the electric permittivity ε0 and magnetic permeability μ0 of free space. As indicated in the section on electric and magnetic constants, these two quantities are not independent but are related to "c", the speed of light and other electromagnetic waves.

4. Physical Connections to ε0 and μ0
The electric permittivity is connected to the energy stored
in an electric field. It is involved in the expression for
capacitance because it affects the amount of charge
which must be placed on a capacitor to achieve a certain
net electric field. In the presence of a polarizable medium,
it takes more charge to achieve a given net electric
field and the effect of the medium is often stated in terms
of a relative permittivity.
The magnetic permeability is connected to the energy stored in a magnetic field. It is involved in the expression for inductance because in the presence of a magnetizable medium, a larger amount of energy will be stored in the magnetic field for a given current through the coil. The effect of the medium is often stated in terms of a relative permeability.

5. Electric Field Energy in Capacitor
The energy stored on a capacitor is in the form of energy density in an electric field is given by:
This can be shown to be consistent with the energy stored in a charged parallel plate capacitor

6. Energy in Capacitor
When the switch is closed to connect the battery to the capacitor, there is zero voltage across the capacitor since it has no charge buildup. The voltage on the capacitor is proportional to the charge
Storing energy on the capacitor involves doing work to transport charge from one plate of the capacitor to the other against the electrical forces. As the charge builds up in the charging process, each successive element of charge dq requires more work to force it onto the positive plate. Summing these continuously changing quantities requires an integral.

7. Capacitor Energy Integral
But as the voltage rises toward the battery voltage in the process of storing energy, each successive dq requires more work. Summing all these amounts of work until the total charge is reached is an infinite sum, the type of task an integral is essential for. The form of the integral shown above is a polynomial integral and is a good example of the power of integration.
Transporting differential charge dq to the plate of the capacitor requires work

8. Energy in an Inductor
When a electric current is flowing in an inductor, there is energy stored in the magnetic field. Considering a pure inductor L, the instantaneous power which must be supplied to initiate the current in the inductor is :
so the energy input to build to a final current i is given by the integral :

9. Energy Stored in magnetic field
For the magnetic field the energy density is :
which is used to calculate the energy stored in an inductor
From analysis of the energy stored in an inductor :
the energy density (energy/volume) is:
so the energy density stored in the magnetic field is 

10. Maxwell equations (Integral form)
Static cases
Electric field, (E-field)
electric flux, .
electric flux density, D.
electric flux intensity, E.
permittivity, .
Magnetic field, (H-field).
magnetic flux, .
magnetic flux density, B.
magnetic flux intensity, H.
permeability, .
Flux linkage,

11. Electric Variables and Units
Field intensity, E (V/m)
Flux density, D (C/m2)
Flux, Y (Coulombs) (C)
Charge, Q (C)
Line charge density, l (C/m)
Surface charge density, s (C/m2)
Volume charge density, r (C/m3)
Capacitance, C (Farads) (F)
C = Q / V (F)

12. Electric field intensity
The force experience by any two charged bodies is given by Coulomb’s law.
Coulomb’s force is inversely proportional to the square of distance.
Electric field intensity, E, is defined in terms of the force experienced by a test charge located within the field.
We could solve all of the electrostatics with this law as:

13. Gauss’s Law (Basic electrostatic form)
Electric flux is equal to the charge enclosed by a closed surface.
• The closed surface is known as a Gaussian surface
• Integrate the flux density over the Gaussian surface to calculate the flux.
• The flux does not depend on the surface! Use the right one!
The enclosed charge can be either
a point charge or
a charge density such as,

14. Flux density
• Magnetic flux density is equal to the product of the permeability and the
magnetic field intensity, H.
• Magnetic flux density can simplify to flux divided by area.
Equation opposite assumes flux density is
uniform across the area and aligned with
the unit normal vector of the surface!
B = Magnetic flux density (T)
0 = Permeability of free space = 4x(10)-7 (H/m)
r = Relative permeability of magnetic material
H = Magnetic field intensity (A/m)
 = Magnetic flux (Wb)

15. Maxwell’s Static Fields
Electrostatic
Maxwell’s 1st Equation = Faraday’s Law
Maxwell’s 3rd Equation = Gauss’s Law
No Electric fields without charges
Magnetostatics
Maxwell’s 2nd Equation = Ampere’s Law
No magnetic Field without currents
Maxwell’s 4th Equation = Conservation of
Magnetic Flux

16. Integral Form of Maxwell Equations
Gauss' law for electricity
The electric flux out of any closed surface is proportional to the total charge enclosed within the surface
Gauss' law for magnetism
The net magnetic flux out of any closed surface is zero.
The line integral of the electric field around a closed loop is equal to the negative of the rate of change of the magnetic flux through the area enclosed by the loop
Faraday's law of induction
Ampere's law
In the case of static electric field, theline integral of the magnetic field around a closed loop is proportional to theelectric current flowing through the loop.