The difference of the scalar potential squared and the modulus of the vector potential squared, Φ2 - |A|2, is Lorentz invariant (a Lorentz scalar). why the statement true?
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The difference of the scalar potential squared and the modulus of the vector potential squared, Φ2 - |A|2, is Lorentz invariant (a Lorentz scalar).
why the statement true?
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- Sequentially, wires A, B, and C from the right where 2 A, 4 A, and 6 A are supplied with electric current with A-C distance of 10 cm and A-B distance of 40% of the total distance. Determine the Lorentz force on wire B!Consider a non-relativistic particle moving in a potential U(r). Can either the phase or the group velocity of the particle exceed the speed of light? What happens to the phase velocity vp at the turning point in the potential U(x), where the particle gets reflected and the group velocity vanishes, v - 0?In the previous problem, in a race to the moon, by 3/4ths the distance, light is one or ten meters ahead of the particle. We routinely approximate mass as zero, gamma as infinite, and speed as the speed of light. ("Massless particles" -- gamma and m have to be eliminated from the expressions. Light is a true massless particle.) If a massless particle has momentum 536 MeV/c, calculate its energy in MeV. I attached the previous problem as well for reference.
- In the theory of relativity, the mass M of a particle with velocity v is mo M(v) = V1- v²/c²What is the speed of an electron that has been accelerated from rest through a potential difference (delta V) = +1000 V? Use conservation of energy (delta K + delta U = 0). Remember that delta U = q(deltaV)Solve the following problem using Lorentz transformations: Two jets of material are ejected in opposite directions from the center of a radio galaxy. Both jets move with a speed of 0.750c relative to the galaxy. Determine the speed of one jet relative to the other.
- (b) Write a necessary condition for a transformation (q,p) to (Q,P) to be connonical. Prove that P-2(1+√qcosp)√q sinp:Q-log(1+√qcosp)Show that the following form of Newton's second law satisfies the Lorentz transformation. Assume the force is parallel to the velocity. dv 1 F = m dt [1 – (v²/c²)]³/2A Van de Graaff accelerator utilizes a 50.0 MV potential difference to accelerate charged particles such as protons. (a) What is the velocity of a proton accelerated by such a potential? (b) An electron?
- Problem 2 The relativistic Lagrangian for a particle of rest mass m moving along the x-axis in a potential V(x) is given by 2 L = -mc² 1 V(x) c2 (a) Derive the Euler-Lagrange equation of motion. (b) Show that it reduces to Newton's equation in the limit |*| << c. (c) Compute the Hamiltonian H of the system. Eliminate ȧ from the Hamiltonian by using the equation ƏL p = ax and write H = H(p, x) as a function of x and p only.The Lorentz coordinate transformation assumes that t = t′ at x = x′ = 0. At what other values of x and x′ does t = t′?