Question

A small metal sphere, carrying a net charge of q1 = -2.70 μC , is held in a stationary position by insulating supports. A second small metal sphere, with a net charge of q2 = -7.50 μC and mass 1.70 g , is projected toward q1. When the two spheres are 0.800 m apart, q2 is moving toward q1 with speed 22.0 m/s(Figure 1). Assume that the two spheres can be treated as point charges. You can ignore the force of gravity.

What is the speed of q2 when the spheres are 0.400 m apart?

How close does q2 get to q1?

Answer 1

A)

Applying the law of conservation of energy,

Initial energy = Final energy

(0.5 x 0.0017 x 22^2) + (9 x 10^9 x 2.7 x 7.5 x 10^-12/0.8) = (0.5 x 0.0017 x v^2) + (9 x 10^9 x 2.7 x 7.5 x 10^-12/0.4)

Solving for final velocity 'v'

v = 14.70 m/s

B)

Again using the law of conservation of energy,

Distance, d = k q1 q2/Ei

d = (9 x 10^9 x 2.7 x 7.5 x 10^-12)/(0.6392)

d = 0.285 m

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