Write down the equations for the real electric and magnetic fields for a

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In summary, for a monochromatic plane wave with amplitude E(subscript 0), frequency omega, and phase angle phi=0, we can write down the equations for the real electric and magnetic fields for two different cases. In case a), the wave is traveling in the negative x direction and polarised in the z direction, and in case b), the wave is traveling in the direction from the origin to the point (1,1,1), with polarisation parallel to the xz plane. In both cases, we can sketch the wave and give the explicit Cartesian components of the propagation vector k and the polarisation n-hat. Additionally, the equation for the electric field in case a) is E(subscript Re)=cos

Homework Statement

Write down the equations for the real electric and magnetic fields for a monochromatic plane wave of amplitude E(subscript 0), frequency omega, and phase angle phi=0, that is

a) traveling in the negative x direction and polarised in the z direction
b) traveling in the direction from the origin to the point (1,1,1), with polarisation parallel to the xz plane.

In each case, sketch the wave, and give the explicit Cartesian components of the propagation vector k and the polarisation n-hat.

The Attempt at a Solution

E(subscript Re)=cos(kz)(E(subscript 0 x) cos (omega t) i) + sin (kz)(E(subscript 0 x sin (omega t))

What difference does it make to the equation whether the wave is traveling in the negative x direction or the positive x direction?

A better attempt at the solution?:

E(r,t)= exp (i(kx-omega t))(-E(subscript 0 y)i+E(subscript 0z)j)

Is any of this wrong?

What are the equations for the real electric and magnetic fields?

The equations for the real electric and magnetic fields are known as Maxwell's equations. These are a set of four differential equations that describe the behavior of electric and magnetic fields in space. They are:
1. Gauss's Law for electric fields: ∇ ⋅ E = ρ/ε0
2. Gauss's Law for magnetic fields: ∇ ⋅ B = 0
3. Faraday's Law: ∇ × E = -∂B/∂t
4. Ampere's Law: ∇ × B = μ0(J + ε0∂E/∂t)
where ∇ is the gradient operator, E is the electric field, B is the magnetic field, ρ is the charge density, ε0 is the electric constant, μ0 is the magnetic constant, and J is the current density.

What is the difference between electric and magnetic fields?

Electric and magnetic fields are both types of physical fields that exist in space. Electric fields are produced by electric charges, while magnetic fields are produced by moving electric charges. One key difference between them is that electric fields affect stationary charges, while magnetic fields only affect moving charges. Additionally, electric fields are created by both positive and negative charges, while magnetic fields are only created by moving charges.

How do the equations for electric and magnetic fields relate to each other?

The equations for electric and magnetic fields are closely related and are often referred to as Maxwell's equations. These equations show that changes in electric fields can produce magnetic fields, and vice versa. This relationship is known as electromagnetic induction and is the basis for many modern technologies, such as generators and motors.

What are some real-life applications of these equations?

Maxwell's equations have numerous real-life applications, including in the fields of telecommunications, electronics, and energy production. They are used to understand and design devices such as antennas, transistors, and power generators. These equations also play a crucial role in the development of technologies like wireless communication, satellite navigation, and medical imaging.

Are there any limitations to these equations?

While Maxwell's equations are incredibly powerful and have been extensively tested and verified, they do have some limitations. These equations do not account for the effects of quantum mechanics, which is necessary for understanding the behavior of subatomic particles. Additionally, they do not consider the effects of gravity, which is described by Einstein's theory of general relativity. Scientists continue to work on developing a unified theory that can incorporate all of these concepts.