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Mathematics and Waves

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.

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Mathematics and Waves

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  1. Mathematics and Waves

  2. Waves from the Sun

  3. Electromagnetic Wave

  4. 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

  5. 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 = q v x B

  6. 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 = q E + q v x B • F = [E + v x B] q

  7. Maxwell’s equations • Maxwell's equations are a set of four partial 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

  8. 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.

  9. 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.

  10. Gauss’s Law for Magnetic field • This is the outward magnetic flux integrated over a closed surface is zero.

  11. 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.

  12. 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.

  13. Ampere’s Circuit Law • A changing electric field induces a magnetic field.

  14. 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.

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