The region between two concentric conducting spheres with radii a and b is filled with a conducting material with resistivity rho. (a) show that the resistance between the spheres is given by r=rho4π (1a−1b) (b) derive an expression for the current density as a function of radius, in terms of the potential difference vab between the spheres. (c) show that the result in part (a) reduces to eq. (25.10) when the separation l=b−a between the spheres is small.

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

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