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

Question

An electron is near a positive ion of charge +9e and a negative ion of charge ?8e (see the figure below). (Take a = 4.77
An electron is near a positive ion of charge +9e and a negative ion of charge ?8e (see the figure below). (Take a = 4.77 An electron is near a positive ion of charge +9e and a negative ion of charge ?8e (see the figure below). (Take a = 4.77 mu m, b = 3.92 mu m, and ? = 55.0 degree .) 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.) 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.)

Explanation / Answer

(a) Assume the origin of the x-y axis corresponds with the position of the electron.

The force of the +9e ion on the electron is:
F+9e = K(9e)(- e) / (4.77*10^-6 m)^2 = (8.99*10^9 Nm^2/C^2)(- 9)(1.60*10^-19 C)^2 / (4.77*10^-6 m)^2
F+9e = -9.1 * 10^-17 N {this force points toward the +9e ion, which is the -x direction}

The force of the -8e ion on the electron is:
F-8e = K(-8e)(- e) / (3.92*10^-6 m)^2 = (8.99*10^9 Nm^2/C^2)(8)(1.60*10^-19 C)^2 / (3.92*10^-6 m)^2
F-8e = 1.2 * 10^-16 N {this force points away from the -8e ion, which is ? = 55.6

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