Physics 308 Homework
 RU Links   Radford University   Department of Physics   RU Planetarium   RUSMART pages (weather) Spring 2014 Classes & Info   PHYS 308   PHYS 309   PHYS 450   My daily schedule   My C.V. Summer jobs/internships   NSF REU Program (list of REU sites) Other links   The Nucleus (resources for    physics/astronomy undergrads)   Pre-Health information   R.U.F.R.E.E.Z.I.N.G.    pics from the north pole trip    the picture from the trip   Simple 2-liter water rocket   American Institute of Physics Homework #12: Do not turn these in since there is a test next week (Friday, April 25). Here is a vector with its x-, y- and z-components: A={x3z, y2sin(kx), z^3}. Calculate (a) ∇(∇⋅A), and (b) (-)∇2A. Show all of your steps--no shortcuts. Here is a set of Maxwell-like equations:    ∇xK=-a(∂L/∂t)    ∇xL= b(∂K/∂t)    ∇⋅K=0    ∇⋅L=0    (a) Derive the wave equation for K.    (b) Derive the wave equation for L.    (c) Find the wave speed for these fields in terms of the constants 'a' and 'b.' (a) Evaluate eiπ/8 in terms of its real an imaginary ports. (b) Write i1/6 using an exponential. Here is an electric field traveling in free space: E=zE0ei(ky+ωt) where z is the unit vector in the z-direction. Draw this electric field as it travels. Find the magnetic field B associated with this electric field. The frequency of this wave is f=100MHz. Find the wavenumber 'k' associated with this wave. Here is a magnetic field traveling in free space: B=xB0ei(kz+ωt) where x is the unit vector in the x direction. Draw this magnetic field as it travels. Find the electric field E associated with this magnetic field.    That's all for homework #12.