Electromagnetic radiation is emitted by accelerat- ing charges. The rate at which energy is emitted from an accelerating charge that has charge q and acceleration a is given by 32.51 q 2 a 2 dE = dt 6pP 0 c 3 where c is the speed of light. (a) Verify that this equation is dimension- ally correct. (b) If a proton with a kinetic energy of 6.0 MeV is traveling in a particle accelerator in a circular orbit of radius 0.750 m, what frac- tion of its energy does it radiate per second? (c) Consider an electron orbiting with the same speed and radius. What fraction of its energy does it radiate per second?

Asquare 1m x 1m plate is shown below. all four of its edges are kept at 0 co. at t=0the temperature distribution is given by: y xtsins n75)=.a) using separation of variables determine the temperature distribution t(x,y,t)along the plate at any time t.b) discretize the heat conduction equation +=22222 txtusing a second-order centered difference scheme for the two second derivatives and a first-order forward euler scheme for the first derivative. using von neumann stability analysis, determine the stability criterion for the proposed discretization scheme in terms of , hand t. solve for the maximum allowable time step tmax