Show that f= 2xy+z3+x2j+3xz2 is a conservative force field ,find potential energy, find work done in moving object from (1,_2,1) to ( 3,1,4)

Imagine that someone pushes one marble toward a motionless marble. would there still be action-reaction forces involved in the collision? how might the marbles’ motions be changed? ?

How are series and parallel circuits simililar? both have multiple paths for electrons to travel. both require resistors in their circuits. both require a switch to complete the circuit. both have at least one path for electrons to travel.

The nuclear potential that binds protons and neutrons in the nucleus of an atom is often approximated by a square well. imagine a proton conned in an innite square well of length 105 nm, a typical nuclear diameter. calculate the wavelength and energy associated with the photon that is emitted when the proton undergoes a transition from the rst excited state (n 2) to the ground state (n 1). in what region of the electromagnetic spectrum does this wavelength belong?