Starting with the energy density of an electromagnetic field U = ε0E^2 /2 + B^2 /2µ0...

Starting with the energy density of an electromagnetic field U = ε0E^2 /2 + B^2 /2µ0 and using two of Maxwell equations in free space, show that the rate of change of U is equal to the divergence of the Poyinting vector S, taken with the opposite sign, that is dU/dt = −∇ ∙ S

Expert Solution

genius_generous answered 2 years ago

a. define Electromagnetic field theory and explain 2 engineering applications of electromagnetic field b.why is modulation...

a. define Electromagnetic field theory and explain 2 engineering applications of electromagnetic field b.why is modulation of waves necessary c. differences between bio- savart and amperes law

The potential energy of a magnetic moment in an external magnetic field is U = -...

The potential energy of a magnetic moment in an external magnetic field is U = - ??B. U is smallest when B is parallel to ? and largest when it is antiparallel. Since the magnetic moment of the electron is directed opposite to its spin (because it has a negative charge), the electron’s energy is highest when the spin is parallel to B. The two possible energy states for the electron are the spin up state (ms = 1212) and...

Assume that a stationary electron is a point of charge. What is the energy density u...

Assume that a stationary electron is a point of charge. What is the energy density u of its electric field at radial distances (a) r = 9.30 mm, ( b) r = 9.30 μm, (c) r = 9.30 nm, and (d) r = 9.30 pm? (e) What is u in the limit as r right-arrow 0 (u right-arrow 0 = 1, u right-arrow infinity = 2)?

Derive the energy density for the magnetic field in a solenoid and use that result along...

Derive the energy density for the magnetic field in a solenoid and use that result along with the result for the electric energy density derived in class to find the time dependent Poynting vector.

2. (a) What is an electromagnetic wave? (b) Draw a visual representation of an electromagnetic wave....

2. (a) What is an electromagnetic wave? (b) Draw a visual representation of an electromagnetic wave. (c) What is the speed of an electromagnetic wave?

Let U be distributed as Uni(0,1). Find the density of U^n for n = 1, 2,...

Let U be distributed as Uni(0,1). Find the density of U^n for n = 1, 2, 3.... and also for n = -1, -2, ....

What is SWF= U(A)+U(B)? , Min[U(A), U(B)] and U(A)*U(B)? Is there a policy?

1 a) What is the approximate electric field strength and magnetic field strength of the electromagnetic...

1 a) What is the approximate electric field strength and magnetic field strength of the electromagnetic waves radiated by a 60-W lightbulb, as measured 5.5 m from the bulb? You can assume that the bulb is 100% efficient in converting electrical energy to light energy. b.) Incandescent light bulbs are very inefficient. Find the electric field strength and magnetic field strength assuming 5% efficiency. Please show all work, thank you!

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 energy E of a magnetic moment ~µ in a magnetic field B~ is E =...

The energy E of a magnetic moment ~µ in a magnetic field B~ is E = −~µ · B~ . Consider an isolated particle with magnetic moment ~µ. The projection of ~µ along z can only take two values: (~µ)z = ±µB, where µB is a constant called the Bohr magneton. i) What are the particle energies E± corresponding to the two projections when the particle is subject to a magnetic field B~ ≡ (0, 0, Bz) along the z-axis...

Question