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27 Nov 2019
According to classical electromagnetic theory anacceleratedelectron radiates energy at the rateKe2a2/c3, where K =6 x109Nm2/C2, e = electronic charge(C), a = instantaneousacceleration (m/sec2), and c =speed of light (m/sec).
a) If an electron were oscillating along a straight linewithfrequency v (Hz) and amplitude A, how much energy would itradiateaway during 1 cycle? (Assume that the motion isdescribedadequately by x = Asin2pvt during any one cycle.)
b) What is the Q of this oscillator?
c) How many periods of oscillation would elapse before the energyofthe motion was down to half the initial value?
d) Putting for v a typical optical frequency (i.e., forvisiblelight) estimate numerically the approximate Q and"half-life" ofthe radiating system.
According to classical electromagnetic theory anacceleratedelectron radiates energy at the rateKe2a2/c3, where K =6 x109Nm2/C2, e = electronic charge(C), a = instantaneousacceleration (m/sec2), and c =speed of light (m/sec).
a) If an electron were oscillating along a straight linewithfrequency v (Hz) and amplitude A, how much energy would itradiateaway during 1 cycle? (Assume that the motion isdescribedadequately by x = Asin2pvt during any one cycle.)
b) What is the Q of this oscillator?
c) How many periods of oscillation would elapse before the energyofthe motion was down to half the initial value?
d) Putting for v a typical optical frequency (i.e., forvisiblelight) estimate numerically the approximate Q and"half-life" ofthe radiating system.
