Suppose there is an electron, floating unattached in empty space, illuminated by

Question

Suppose there is an electron, floating unattached in empty space, illuminated by the laser beam from a big laser. The oscillating electric field of the laser exerts a force on the electron, causing it to wiggle back and forth in space. Using F = ma, and knowing the force exerted on a charge by an electric field, we can determine the maximum velocity Vmax of the wiggling electron. Obviously, the larger is the E-field of the laser, the larger is Vmax. We showed in lecture that we can neglect the force exerted by the B-field as long as the velocity of the charges is much smaller than the speed of light. So how large does the E-field have to be in order to make the electron reach a velocity that is only 0.1% of the speed of light? For E-fields larger than that, our approximation of neglecting the effects of the B-field might not be valid. (You can assume that the laser wavelength is 532 nm.)

Explanation / Answer

E is the electric field on the electron Work done by the electric field W = qED where q is charge and D is the distance This work will give Kinetic energy of 1/2mv^2 to the electron Here v is v(max) = 0.1% of speed of light = 3 x 10^5 X10^-3 = 300 KM/s = 3 X 10^5 m/s so qED = 1/2 mv(max)^2 E = 1/2 (m/q) v(max)^2/D = 1/2 (0.571 X 10^-11) (3 X10^5)^2/(532 X10^-9) =4.8 X 10^5 N/C

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