A small metal sphere, carrying a net charge of q 1 = 2.80 µC, is held in a stati

Question

A small metal sphere, carrying a net charge of q1 = 2.80 µC, is held in a stationary position by insulating supports. A second small metal sphere, with a net charge of q2 = 2.60 µC and mass 2.00 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 (see figure below). Assume that the two spheres can be treated as point charges. You can ignore the force of gravity.

(a) What is the speed of q2 when the spheres are 0.400 m apart?
(b) How close does get q2 to q1?

Explanation / Answer

given,

q1 = -2.8 uC

q2 = -2.6 uC

mass of small sphere = 2 g

initial distance = 0.8 m

final distance = 0.4 m

by conservation of energy

initial energy = final energy

initial energy = initial kinetic energy + initial electric potential energy

final energy = final kinetic energy + final electric potential energy

electric potential energy = k * q1 * q2 / r

kinetic energy = 0.5 * mv^2

0.5 * 2 * 10^-3 * 22^2 + 9 * 10^9 * 2.8 * 10^-6 * 2.6 * 10^-6 / 0.8 = 0.5 * 2 * 10^-3 * v^2 + 9 * 10^9 * 2.8 * 10^-6 * 2.6 * 10^-6 / 0.4

v = 20.05 m/s

speed of q2 when q2 is 0.4 apart = 20.05 m/s

when q2 stops moving its final kinetic energy will be 0

so,

0.5 * 2 * 10^-3 * 22^2 + 9 * 10^9 * 2.8 * 10^-6 * 2.6 * 10^-6 / 0.8 = 9 * 10^9 * 2.8 * 10^-6 * 2.6 * 10^-6 / x

x = 0.11578 m

q2 can get 0.11578 m close to q1

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.