Derive wave equations or the electric field and magnetic field in vacuum. (Refer to Griffiths "Introduction...

Derive wave equations or the electric field and magnetic field in vacuum.

(Refer to Griffiths "Introduction to electrodynamics" Chapter 9.2.1)

Expert Solution

genius_generous answered 2 years ago

The electric field of an electromagnetic wave that propagates in a vacuum is given by: ?⃗...

The electric field of an electromagnetic wave that propagates in a vacuum is given by: ?⃗ (?, ?) = 2 cos (α? - ω?) ? + 2 sin (α? - ω?) ?, ?? (?/?); ???? α ? ω ??? ?????????? a) What is the amplitude E0 of the electric field, its angular frequency, period, frequency f, wave number | ?⃗ |, wavelength, its speed u and its phase constant φ? b) I) Determine the electric field in the x-y plane...

The magnetic field of a uniform plane wave that propagates in a vacuum, is given by...

The magnetic field of a uniform plane wave that propagates in a vacuum, is given by the expression: B (r, t) = (10^−6 )[xˆ + 2yˆ + Bzzˆ] cos [ωt + 3x - y - z] in m.k.s.units and where xˆ, yˆ, zˆ are unit vectors along the cartesians axes . Find: (a) The propagation direction. (b) The wavelength λ. (c) The angular frequency ω. (d) The associated electrical field

Write an equation for the magnetic field of an electromagnetic wave traveling in vacuum if the...

Write an equation for the magnetic field of an electromagnetic wave traveling in vacuum if the amplitude is 0.0028 T and the frequency is 2.0 × 108 Hz. Find the magnetic field when x = 32 cm and t = 6.8 ns.

The components of the electric field in an electromagnetic wave traveling in vacuum are described by...

The components of the electric field in an electromagnetic wave traveling in vacuum are described by Ex = 0, Ey = 0, and Ez = 2.84 sin(8.73x - ωt) V/m, where x is measured in meters and t in seconds. Calculate the frequency of the wave. Tries 0/99 Calculate the wavelength of the wave. Tries 0/99 Calculate the amplitude of the magnetic field of the wave. Tries 0/99 Calculate the intensity of the wave. Tries 0/99

Derive the electromagnetic wave equation in terms of the magnetic field H

A plane electromagnetic wave with magnetic field amplitude 0.02 T is propagating through a vacuum. What...

A plane electromagnetic wave with magnetic field amplitude 0.02 T is propagating through a vacuum. What is the electric field amplitude? B) What is the magnitude of the Poynting vector? C. If the wavelength is 500 nm what is the wave frequency and the energy of a single photon? D. How many of these photons must pass through a square meter each second to yield the power flux calculated in part B?

Prove that Maxwell’s equations yield the wave equation for the electric field [HINT: ∇ × (∇×...

Prove that Maxwell’s equations yield the wave equation for the electric field [HINT: ∇ × (∇× ) = ∇(∇·) − ∇ · ∇]

Explain the steps to obtaining an electric field, magnetic field, electric flux, and magnetic flux.

These questions refer to the expression for the magnetic field at the center of the square...

These questions refer to the expression for the magnetic field at the center of the square solenoid. Assume: for all coils, each side of the square a = 4.87 cm and the length of the solenoid L = 47.8 cm. NOTE: Everything must be in MKS units! NOTE: μo = 1.26x10-6 in MKS units (determined in question 1). a) In procedure 1, you will plot Bmax vs. N, the number of turns of the coil. Suppose you set the current...

What are the basic similarities and differences between an electric field and a magnetic field?

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