What property of Maxwells equations results in electromagnetic waves?
A. Moving charges create B
B. There are no magnetic monopoles
C. delta E/Delta t creates B and delta B/delta T creates E
D. Charges create E and currents create B
The property of Maxwell's equations that results in electromagnetic waves is option C: delta E/Delta t creates B and delta B/delta t creates E.
To understand why this is the case, we need to look at Maxwell's equations. These equations are a set of four fundamental equations that describe how electric and magnetic fields interact. They were formulated by James Clerk Maxwell in the 19th century and are the foundation for the theory of classical electromagnetism.
The first two equations, known as Gauss's laws, describe how electric fields and magnetic fields are created by electric charges and magnetic currents. Gauss's law for electric fields states that the electric flux through a closed surface is proportional to the charge enclosed by that surface. Gauss's law for magnetic fields states that the magnetic flux through a closed surface is always zero, indicating that there are no magnetic monopoles (option B).
The third equation, known as Faraday's law, states that a changing magnetic field induces an electric field. Mathematically, this is represented by the equation delta B/delta t = -mu0 * epsilon0 * delta E/delta t, where delta E/delta t represents the rate of change of electric field with time, delta B/delta t represents the rate of change of magnetic field with time, mu0 is the permeability of free space, and epsilon0 is the permittivity of free space. This equation shows that a changing magnetic field creates an electric field.
Conversely, the fourth equation, known as Ampere's law with Maxwell's addition, states that a changing electric field induces a magnetic field. Mathematically, this is represented by the equation delta E/delta t = (1/c^2) * delta B/delta t, where delta E/delta t represents the rate of change of electric field with time, delta B/delta t represents the rate of change of magnetic field with time, and c is the speed of light. This equation shows that a changing electric field creates a magnetic field.
Combining Faraday's law and Ampere's law, we can see that a changing electric field creates a changing magnetic field, and a changing magnetic field creates a changing electric field. This self-generating and self-sustaining nature of electric and magnetic fields gives rise to electromagnetic waves. When electric and magnetic fields oscillate and propagate through space, they create electromagnetic waves, which can travel through a vacuum at the speed of light.
Therefore, option C, delta E/Delta t creates B and delta B/delta t creates E, is the property of Maxwell's equations that explains the generation of electromagnetic waves.