In the figure particles 2 and 4, of charge -e, are fixed in place on a y axis, at y2 = -8.48 cm and y4 = 4.24 cm. Particles 1 and 3, of charge +e, can be moved along the x axis. Particle 5, of charge +e, is fixed at the origin. Initially particle 1 is at x1 = -8.48 cm and particle 3 is at x3 = 8.48 cm. (a) To what x value must particle 1 be moved to rotate the direction of the net electric force on particle 5 by 30 degrees counterclockwise?
(b) With particle 1 fixed at its new position, to what x value must you move particle 3 to rotate back to its original direction?

Consider the particle-in-a-box problem in 1d. a particle with mass m is confined to move freely between two hard walls situated at x = 0 and x = l. the potential energy function is given as (a) describe the boundary conditions that must be satisfied by the wavefunctions ψ(x) (such as energy eigenfunctions). (b) solve the schr¨odinger’s equation and by using the boundary conditions of part (a) find all energy eigenfunctions, ψn(x), and the corresponding energies, en. (c) what are the allowed values of the quantum number n above? how did you decide on that? (d) what is the de broglie wavelength for the ground state? (e) sketch a plot of the lowest 3 levels’ wavefunctions (ψn(x) vs x). don’t forget to mark the positions of the walls on the graphs. (f) in a transition between the energy levels above, which transition produces the longest wavelength λ for the emitted photon? what is the corresponding wavele

Estimate the schwarzschild radius (in kilometers) for a mini-black hole formed when a superadvanced civilization decides to punish you (unfairly) by squeezing you until you become so small that you disappear inside your own event horizon. (assume that the your weight is 50 kg)

If two parallel light rays hit a mirror, they will not be parallel to each other after they reflect.