It is shown in more advanced courses that charged particles in circular orbits radiate electromagnetic waves, called cyclotron radiation. As a result, a particle undergoing cyclotron motion with speed vis actually losing kinetic energy at the rate dK/dt=−(μ_0*q^4/6πcm^2)B^2v^2
a. How long does it take an electron to radiate away half its energy while spiraling in a 1.5 T magnetic field?
b. How long does it take a proton to radiate away half its energy while spiraling in a 1.5 T magnetic field?

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Asquare isothermal chip is of width w=5 mm on a side and is mounted in a substrate such that its side and back surfaces are well insulated; the front surface is exposed to the flow of a coolant at tinf=15 °c. from reliability considerations, the chip temperature must not exceed t=85 °c. if the coolant is air and the corresponding convection coefficient is h=200 w/m2 x k, what is the maximum allowable "power" of the chip? if the coolant is a liquid for which h=3000 w/m2 x k, what is the maximum allowable power of the chip?

Zamir and talia raced through a maze. zamir walked 2 m north, 2 m east, 4 m south, 2 m east, 4 m north, 2 m east, 3 m south, 4 m east and 4 m north. talia walked 2 m north, 6 m east, 3 m south, 4 m east, and 4 m north. compare their displacements: zamir's displacement is talia's displacement.