In a cathode-ray tube (CRT), an electron travels in a vacuum and enters a region

Question

In a cathode-ray tube (CRT), an electron travels in a vacuum and enters a region between two "deflection" plates which have equal and opposite charges. The dimensions of each plate are L = 12 cm by d = 5 cm, and the gap between them is h = 2.5 mm A drawing of the diagram can be found here: http://www.webassign.net/mi3/16-056-cathode_ray_tube_sym.jpg During a 0.001 s interval while it is between the plates, the change of the momentum of the electron ?parrowitalic is < 0, -7.20e-17, 0 > kg m/s. a) What is the electric field between the plates? Hint: remember the Momentum Principle (the relationship between Impulse and change in momentum.) b) What is the charge (both magnitude and sign) of the upper plate?

Explanation / Answer

The force on the electron is qE (neglecting weight) and that's equal to the rate of change of momentum; E = (1/q)(deltaP/t) = (1/- 1.6x10^-19)(6.4x10^-17)/.001 = For large plate area compared to plate separation the plate charge density "D" is uniform and related to the magnitude of the E field as; (on either plate) E = D/e(o) = Q/Ae(o) = Q/Lde(o) Q = ELde(o) = (4x10^5)(.12)(.05)(8.85x10^-12) =2.124 x 10^-8 C Since the electron's change in momentum was up (positive) it was attracted to the upper plate so the upper plate is positive.

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