Download Mathematics and waves

Waves from the Sun
Electromagnetic Wave
 Electric field – The electric field E at a point is
defined as the force per unit charge experienced by a
small positive test charge placed at that point.
 E = F/q
 Magnetic field – Magnetic field B is also defined in
terms of force, the charge q must be moving in order
for magnetic forces to be acting.
 F=qvxB
Lorentz force
 In physics, the Lorentz force is the force on a point
charge due to electromagnetic fields. It is given by the
following equation in terms of the electric and
magnetic fields.
 F=qE+qvxB
 F = [E + v x B] q
Maxwell’s equations
 Maxwell's equations are a set of four partial
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differential equations describing how the electric and
magnetic fields relate to their sources, charge density
and current density, and how they develop with time.
Gauss’s Law for Electric Fields
Gauss’s Law for Magnetic Fields
Faraday’s Law of Induction
Ampere’s Circuit Law
Gauss’s Law for Electric Fields
 The outward electric flux integrated over a closed
surface is proportional to the net electrical charge
enclosed by the surface.
 Outward flux is defined so that field lines leaving the
closed surface contribute positively while field lines
entering the closed surface contribute negatively.
Application
 Gauss's law is very helpful in calculating electric field
in those cases where electric field is symmetrical
around the source producing it. Eq- spherical,
cylindrical, or planer symmetry.
Gauss’s Law for Magnetic field
 This is the outward magnetic flux integrated over a
closed surface is zero.
Faraday’s Law of Induction
 A changing magnetic field induces an electric field.
For a curve C that bounds an area A.
 Faraday's law of induction is a basic law of
electromagnetism relating to the operating principles
of transformers, inductors, and many types of
electrical motors and generators.
Example
 A cylindrical region of space of radius R contains a
uniform magnetic field B with direction into the page,
as in fig. If the magnitude changes in time, describe
the induced electric field for points inside the cylinder.
Ampere’s Circuit Law
 A changing electric field induces a magnetic field.
Conclusion
 Together with the Lorentz force law, these equations
form the foundation of classical electrodynamics,
classical optics, and electric circuits.
 These in turn underlie the present radio, television,
phone, generators, information-technologies etc.
 The Maxwell equations have also been the starting
point for the development of relativity theory by
Albert Einstein because they predict the existence of a
fixed speed of light, independent of the speed of the
observer.