The electromagnetic field is invariant under a gauge transformation of the scalar and vector potential given by a rightarrow a + psi (r, t), phi rightarrow phi - l / c psi / t, where psi is arbitrary (but differentiable). what effect does this gauge transformation have on the lagrangian of a particle moving in the electromagnetic field? is the motion affected?

Aball is thrown upward in the air, and its height above the ground after t seconds is h ( t ) = 57 t − 16 t 2 feet. find the time t when the ball will be traveling upward at 14.25 feet per second.

Estimate the change in the gibbs energy and molar gibbs energy of 1.0dm3 of octane when the pressure acting on it is increased from 1.0 atm to 100 atm. the mass density of octane is 0.703 g cm−3

Neutrons are placed in a magnetic field with magnitude 2.30 t. part a part complete what is the energy difference between the states with the nuclear spin angular momentum components parallel and antiparallel to the field? δe δ e = 2.77×10−7 ev previous answers correct part b part complete which state is lower in energy: the one with its spin component parallel to the field or the one with its spin component antiparallel to the field? which state is lower in energy: the one with its spin component parallel to the field or the one with its spin component antiparallel to the field? parallel antiparallel previous answers correct part c part complete how do your results compare with the energy states for a proton in the same field (δe=4.05×10−7ev)? how do your results compare with the energy states for a proton in the same field this result is smaller than but comparable to that found in the example for protons. this result is greater than but comparable to that found in the example for protons. previous answers correct part d the neutrons can make transitions from one of these states to the other by emitting or absorbing a photon with energy equal to the energy difference of the two states. find the frequency of such a photon. f f = mhz previous answersrequest answer incorrect; try again; 5 attempts remaining