A particle with charge q moves in the x direction with constant velocity v with respect to a reference frame S. Determine the electric and magnetic field recorded by an observer in S at an arbitrary point (x, y, z). Assume that the charge passes through the origin x = 0 at t = 0.
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A particle with charge q moves in the x direction with constant velocity v with respect to a reference frame S. Determine the electric and magnetic field recorded by an observer in S at an arbitrary point (x, y, z).
Assume that the charge passes through the origin x = 0 at t = 0.
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- v HĽ (b) System S is moving to the left at speed v = 0.8 c relative to S. Find the force on the charge q as measured in S. Do it in 2 ways.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]?In an inertial reference frame S there is only a uniform electric field →, →→, = 8 kVm-¹. Find the magnitude of E' and B'in the inertial reference frame S' moving with a constant velocity v relative to the frame S at an angle a = 45° to the vector E. The velocity of the frame S' is 0-6 times the velocity of light c. E
- Determine an expression for the total travel time of the light pulse, as measured by the following: A) an observer in the S frame (Use the following as necessary: c, d, and v.) B) an observer on the spacecraft (Use the following as necessary: c, d, and v.) What If? If the transmitted light beam has a wavelength λT, determine an expression for the shift in the wavelength of the light beam, as measured by the following C) an observer in the S frame (Use the following as necessary: c, v, and λT.) D) an observer on the spacecraft (Use the following as necessary: c, v, and λT.)As shown in the figure, a stationary mirror is mounted in a reference frame S and a space shuttle moves toward the mirror at a speed v = 0.590c relative to the reference frame S. The instant the shuttle is a distance d = 5.00 × 10¹0 m from the mirror (as measured by an observer in S), it emits a light pulse that travels to the mirror and is reflected back to the shuttle. Determine the total travel time (in s) for the light pulse as seen by the following. (a) an observer in the S reference frame S (b) an observer on the shuttle S What If? If the light beam has an initial wavelength of 530 nm, determine the shift (in nm) in the wavelength of the light beam as measured by the following (use + for an increase and decrease). (c) an observer in the S frame nm Mirror (d) an observer on the shuttle nm for aSuppose two angry rhinoceros charge each other. According to a few observers on the ground, the rhinoceros on the left moved to the right at a speed of (1 - ϵ)c while the rhinoceros on the right moved to the left at a speed of (1 - ϵ)c. ϵ is in the range of 0 < ϵ < 1. How fast is the rhinoceros on the right moving in the frame of the rhinoceros on the left? (Show that this speed is less than c, no matter how small ϵ is)
- You have been posted to a remote region of space to monitor traffic. Near the end of a quiet shift, a spacecraft streaks past. Your laser-based measuring device reports the spacecraft’s length to be 85 m. The identification transponder reports it to be the NCXXB-12, a cargo craft of proper length 100 m. In transmitting your report to headquarters, what speed should you give for this spacecraft?At the Fermilab accelerator in Weston, Illinois, singly charged ions with momentum 3.3 × 10−16 kg m/s are held in a circular orbit of radius 1.00 km by an upward magnetic field. What B field must be used to maintain the ions in this orbit? (qion = 1.60 × 10−19 C)When pions are brought to rest their lifetime is 1.77´10-8 s. A beam of pions is produced in an accelerator and moves at a speed of 0.99c relative to the laboratory. After moving 39 m as measured in the la, half the pions have decayed. a) from the viewpoint of an observer in the lab frame and b) from an observer at rest in the frame of the moving pions that the two numerical results given in the problem for the half-life of the pions are consistent.
- Einstein concluded that the speed of light is the same in all inertial frames. Prove that the analysis of the Michelson-Morley experiment (see attached image) is in error.At t=0, an alien spaceship passes by the earth: let this be event A. At t=13 min (according to synchronized clocks on earth and Mars), the spaceship passes by Mars, which is 5 light-minutes from earth at the time: let this be event B. Radar tracking indicates that the spaceship moves at a constant velocity between earth and Mars. Just after the ship passes earth, people on earth launch a probe whose purpose is to catch up with and investigate the spaceship. This probe accelerates away from earth, moving slowly at first, but moving faster and faster as time passes, eventually catching up with and passing the alien ship just as it passes Mars. In all parts of this problem, you can ignore the effects of gravity and the relative motion of earth and Mars (which are small) and treat earth and Mars as if they were both at rest in the inertial reference frame of the solar system. Also assume that both the probe and the alien spacecraft carry clocks. 1. Draw a quantitatively accurate…Events 1 and 2 are exploding firecrackers that each emit light pulses. In the reference frame of the detector, event 1 leaves a char mark at a distance 3.40 m from the detector, and event 2 leaves a similar mark at a distance 2.10 m from the detector. If the two events are simultaneous in the reference frame of the detector and occur at instant t = 0, at what instant of time will each light pulse be detected?