Do the following problem two ways, first use classical physics and then use rela

Question

Do the following problem two ways, first use classical physics and then use relativity. For both methods use conservation of energy. Do not find velocity as a function of time. An electron starts from rest a distance of 1.0 cm away from a point charge with Q = -3.0 mCoul which is at rest the origin. How fast is it moving when it reaches r = infinity. To do this problem classically use conservation of energy. Use the potential energy function for electrostatics etc. In order to do this for relativity remember that the gamma factor is not constant and you do not care what its time dependence is, only the final value. You know the initial value of gamma. The gamma factor does not affect the potential energy function. The conserved quantity in relativity is E = gamma m_0 c^2 + PE

Explanation / Answer

using conservation of energy

Q = charge placed at some distance = - 0.003 C

q = charge on electron = 1.6 x 10-19 C

r = distance = 10 cm = 0.1 m

electric potential energy = kinetic energy of electron

k Q q/r = (0.5) m v2

(9 x 109) (- 0.003) (- 1.6 x 10-19) = (0.5) (9.1 x 10-31) v2

v = 3.1 x 109 m/s

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