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 1.80 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.

Part A

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

Part B

How close does q2 get to q1?

Answer 1

Initially, total energy E = U + KE = kQq / d + ½mv²
E = 8.99e9N·m²/C² * -2.7e-6C * -7.5e-6C / 0.8m + ½ * 0.0018kg * (22m/s)²
E = 0.663 J
At r = 0.4 m

U = 0.182N·m² / 0.4m

U= 0.455 J
so the remaining
KE = (0.663 - 0.455)J

0.208 J = ½ * 0.0018kg * v²
V= 15.20 m/s

(b) U = 0.663 J

0.663 J= 0.182N·m² / r
r= 0.275 m

Note that 8.99e9N·m²/C² * -2.7e-6C * -7.5e-6C = 0.182N·m²

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