An electron is near a positive ion of charge +9e and a negative ion of charge 8e

Question

An electron is near a positive ion of charge +9e and a negative ion of charge 8e (see the figure below). (Take a = 3.81 µm, b = 3.72 µm, and = 65.0°.)

An electron is near a positive ion of charge +9e and a negative ion of charge ?8e (see the figure below). (Take a = 3.81 mum, b = 3.72 mum, and theta = 65.0degree.) (a) Find the magnitude and direction of the resultant force on the electron. (Let right be the +x-direction. Measure the angle counter-clockwise from the +x-axis.) magnitude direction degree (b) Find the magnitude and direction of the electron's instantaneous acceleration (Let right be the +x-direction. Measure the angle counter-clockwise from the +x-axis.) magnitude direction degree

Explanation / Answer

a = 3.81 µm, b = 3.72 µm, = 65.0o, c = 3.00 m

(a) force on the electron due to +9e is -k*9e*e/a2 i

force on the electron due to -8e is k*8e*e/c2 (cos i - sin j)

net force on the electron = ke2[(-9/a2 + 8cos/c2) i - 8sin/c2 j] = (-5.63*10-17 i - 1.86*10-16 j) N/C

magnitude = 1.94*10-16 N/C
direction = 180 + tan-1(1.86*10-16/5.63*10-17) = 253°

(b) the electron's instantaneous acceleration a = F/m
magnitude = 2.13*1014 m/s2
direction = 253°

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