A small metal sphere, carrying a net charge of q_1 = -2.80 mu C, is held in a st

Question

A small metal sphere, carrying a net charge of q_1 = -2.80 mu C, is held in a stationary position by insulating supports. A second small metal sphere, with a net charge of q_2 = -3.60 mu C and mass 1.30 g, is projected toward q_1. When the two spheres are 0.800 m apart, q_2 Is moving toward q_1 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. What is the speed of q_2 when the spheres are 0.400 m apart? How close does get q_2 to q_1?

Explanation / Answer

step;1

Given that

charge q1=-2.8*10^%-6 C

charge q2=-3.6*10^-6 c

speed u=22 m,/s

initial distance xi=0.8 m

step;2

now we find the electric field

the electric field E=9*10^9*-3.6*10^-6/(0.8)^2=-50.63*10^3 N/c

step;3

now we find the speed at distance 0.4 m

speed V^2=22^2+2*-3.6*10^-6*-50.63*10^3*0.4/1.3*10^-3

=484+1121.6

=1605.6

speed of q2=40.1 m/s

step;3

now we find the distance q2 to q1

distance x=0.8/[3.6/2.8]^1/2+1

=0.8/2.1

=0.4 m

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