Problems on Electromagnetic Waves - Assignment | PHYS 260, Assignments of Physics

Download Problems on Electromagnetic Waves - Assignment | PHYS 260 and more Assignments Physics in PDF only on Docsity! EM Waves Homework Set Problem 1. a) The wavelength of the most energetic x rays produced when electrons are accelerated to a kinetic energy of 18 GeV in the Stanford Linear Accelerator and then slam into a solid target is 0.067 fm. What is the frequency of these x-rays? Convert relevant quantities to SI units Write the expression between the speed of light and the frequency and wavelength of light. Calculate the frequency of the x-rays. b) A VLF (very low frequency) radio wave has a frequency of only 30 Hz. What is its wavelength? Calculate the wavelength of the radio waves. EM Waves Homework Set Problem 2. What inductance must be connected to a 17 pF capacitor in an oscillator capable of generating 550 nm (visible) electromagnetic waves? Convert relevant quantities to SI units Write the expression between resonant frequency and capacitance and inductance. Calculate the frequency of the light. Set the resonant frequency equal to the frequency of the light. Solve for inductance. EM Waves Homework Set Problem 4. Show that E=Em sin(kx-ωt) is a solution of the wave equation where k=2π/λ and ω=2πf. Find the first derivative of E with respect to time. Find the second derivative of E with respect to time. Find the first derivative of E with respect to position. Find the second derivative of E with respect to position. Insert these second derivatives into the wave equations and show equivalence. EM Waves Homework Set Problem 5. A helium-neon laser, radiating at 632.8 nm, has a power output of 3.0 mW and full angle beam divergence of 0.17 mrad. a) What is the intensity of the beam 40 m from the laser? The full beam angle of divergence is entire angular spread of the beam. Use the chord-length expression (s=rθ) to calculate full width of the beam at 40 m. The intensity is calculated by dividing the source power by the area of circle which has the diameter of the full width of the beam at 40 m. Calculate the intensity. b) What is the power of a point source that provides the same intensity at the same distance? The intensity of a point source is defined as the power from the point divided by 4*π*distance2. Write a mathematical expression for this and solve it for the power. Use the numerical values previously calculate to determine the power. EM Waves Homework Set Problem 6. A plane magnetic wave with a wavelength of 3.0 m travels in vacuum in the positive x-direction with its electric field vector E, of amplitude 300 V/m, directed along the y-axis. a) What is the frequency f of the wave? Use the speed of light to calculate the frequency. b) What are the direction and amplitude of the magnetic field associated with the wave? Use the relationship between the speed of light and electric and magnetic field amplitudes to calculate the magnetic field amplitude. Use the relationship of the Poynting vector to electric field vector to discuss the magnetic field direction. c) If E=Em sin(kx –ωt), what are values of k and ω? Calculate k and ω.