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 = -7.30 mu C and mass 2.00 g, is projected Coward 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. (a) what is the speed of q_2 when the spheres are 0.400 m apart? m/s (b) How close does get q_2 to q_1? m

Explanation / Answer

here,

q1 = - 2.8 * 10^-6 C

q2 = - 7.3 * 10^-6 C

mass , m = 0.002 kg

v0 = 22 m/s and r0 = 0.8 m

a)

let the speed of q2 when r = 0.4 m be v

using conservation of energy

0.5 * m * v0^2 + k * q1*q2/r0 = 0.5 * m * v^2 + k * q1*q2/r

0.5 * 0.002 * 22^2 + 9 * 10^9 * 10^-12 * 2.8 * 7.3 /0.8 = 0.5 * 0.002 * v^2 + 9* 10^9* 10^-12 * 2.8* 7.3 /0.4

solving for v

v = 16 m/s

b)

let the closest distance be r when v = 0 m/s

using conservation of energy

0.5 * m * v0^2 + k * q1*q2/r0 = 0.5 * m * v^2 + k * q1*q2/r

0.5 * 0.002 * 22^2 + 9 * 10^9 * 10^-12 * 2.8 * 7.3 /0.8 = 9* 10^9* 10^-12 * 2.8* 7.3 /r

solving for r

r = 0.26 m

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