A microscopic spherical dust particle of radius r and mass m is moving in outer space at a constant speed v. A wave of light strikes it from the opposite direction of its motion and gets absorbed. Part A) Assuming the particle decelerates uniformly to zero speed in time t, write an equation for the average electric field amplitude in the light.

A microscopic spherical dust particle of radius r and mass m is moving in outer space at a constant speed v. A wave of light strikes it from the opposite direction of its motion and gets absorbed. Part A) Assuming the particle decelerates uniformly to zero speed in time t, write an equation for the average electric field amplitude in the light.

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Let's try a few more examples that relate power and energy. A certain high-efficiency LED light bulb has a power output of 9.20 W. That is, 9.20 J of electric energy is converted to electromagnetic (light) energy and radiated away every second. How much energy is output by the lightbulb if it is left on for a total time of 7.50 hours? In this case, we're relating power to energy change, so we simply use the relationship E t P = Here, instead of work W, we use in the equation E, which is the amount of energy output or converted in the amount of time t. From this, what do we find the total energy output in joules to be? 33120 X x Solve the above equation for the energy E in terms of power P and time t. Remember that 1 W = 1 J/s, so to find the energy in joules, convert the time to seconds first. There are 60 minutes in one hour and 60 seconds in one minute. J
We have a plane electromagnetic wave traveling in the +z direction. As you may recall, plane waves have electric and magnetic fields that vary like either sine or cosine, with an argument of (kz−ωt). Our goal here will be to write down the equations describing the electric and magnetic fields in this particular wave, and then use those equations to calculate a few quantities.Let's suppose that at z=0 and t=0, the magnetic field has its maximum value B0 and points in the −y direction. Use that information to decide whether your B -field should vary like sine or like cosine, and write a symbolic vector expression for B . Then write a symbolic vector expression for the E -field that would be in this wave. The definition of the Poynting vector will let you figure the direction of the E -field. A) The frequency of this wave is f=3.060e+06 Hz. What is the scalar value of the magnetic field at t=1.29e−07 s? You can still assume that z=0, and that B0 = .0056 T . For m answer I got .0059 T…
A microscopic spherical dust particle of radius r and mass m is moving in outer space at a constant speed v. A wave of light strikes it from the opposite direction of its motion and gets absorbed. Assuming the particle decelerates uniformly to zero speed in time t, write an equation for the average electric field amplitude in the light.
A plane wave is propagating at a frequency of 100 MHz in a lossy medium. The amplitude of the electric field E at z=0 is equal to 200V/m. The medium is characterized by u=1 and &=2. 1. Find the propagation constant y after 1m: the amplitude of E loses 60% of its value and the its phase angle changes of 180'. 2. Find the conductivity a 3. Find the real and complex notations of the electric field 4. Find the expression of the magnetic field H 5. Deduce D and B 6. Find the expression of the Poyting vector 7. Find its average with respect to t.
Problem 1. In class we will consider the sum of the electric field of two plane waves, u:(z.t) and uz(z.t), both traveling in the positive z direction with slightly different frequencies and propagation constants and with equal amplitudes. The electric fields of both plane waves are oriented in the y direction, which means that they have the same "polarization". The time and space variation of the two electric fields are given by: u: (2.1) = cos(@t - kz) uz(2.1) = cos ([o + Ao]t - [k + Ak]2) We will show that the sum of these two waves produce an intensity envelope in time and space that modulates the carrier frequency of m + Ao/2. The velocity of the envelope is called the group velocity. Assume Ao is << than o. For this problem, consider the sum of two slightly different waves with similar electric fields: v.(z) = sin(ot - kz) vz(z1) = sin([o + Ao]t - [k + Ak]z) Derive analytically an expression for a) the group and b) the phase velocity for the sum of the two fields. HINT: sinfa) +…
Acceleration in a cyclotron. Suppose in a cyclotron that B = 2B and E₂ = E cos w t E = - E sin w t E = 0 with E constant. (In an actual cyclotron the electric field is not uniform in space.) We see that the electric field intensity vector sweeps around a circle with angular frequency w.. Show that the displacement of a particle is described by x(t) = y(t) = qE Mw 2 qE Mw2 (wet sin wet + cos wet- 1) (wet cos wet sin wet) where at t = 0) the particle is at rest at the origin. Sketch the first few cycles of the displacement.
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A speeder tries to explain to the police that the yellow warning lights she was approaching on the side of the road looked green to her because of the Doppler shift. How fast would she have been traveling if yellow light of wavelength 576.6 nm had been shifted to green with a wavelength of 562.3 nm? Note: For speeds less than 0.03c, the equation below will lead to a value for the observed frequency accurate to approximately two significant digits. answer in m/s
Scientists in the laboratory create a uniform electric field Ē = 1.0 x 10°k [V/m] in a region of space where B = 0. What are the fields in the reference frame of a rocket travelling in the positive x direction at 1.0 × 106 [m/s]?
Solve, with no calculus.
You are moving at a speed 2/3 c toward Randy when shines a light toward you. At what speed do you see the light approaching you? a 1/3 c b 2/3 c c 4/3 c d c
Large quantities of dust should have been left behind after the creation of the solar system. Larger dust particles, comparable in size to soot and sand grains, are common. They create shooting stars when they collide with the earth's atmosphere. But very small dust particles are conspicuously absent. Astronomers believe that the very small dust particles have been blown out of the solar system by the sun. By comparing the forces on dust particles, determine the diameter of the smallest dust particles that can remain in the solar system over long periods of time. Assume that the dust particles are spherical, black, and have a density of 2000kg/m^3. The sun emits electromagnetic radiation with a power of 3.9×10^26W.