Map sapling learning A 28.91-mC charge is placed 35.15 cm to the left of a 83.23

Question

Map sapling learning A 28.91-mC charge is placed 35.15 cm to the left of a 83.23-mC charge, as shown in the figure, and both charges are held s (depicted as a blue sphere) is placed at rest at a distance 31.64 above the right-most charge. If the particle were to be released from rest, it would follow some complicated path around the two stationary charges A particle with a charge of-7.051 C and a mass of 41.31 g Calculating the exact path of the particle would be a challenging problem, but even without performing such a calculation it is possible to make some definite predictions about the future motion of the particle If the path of the particle were to pass through the gray point labeled A, what would be its speed vA at that point? Number 7.051 "A961.12 m/s Tools 31.64 cm +28.91 mC K-10.55cm +83.23 mC 35.15 cm

Explanation / Answer

Potential due to point charge is given as

V = k * q/d

Now , at initial position ,

potential is sum of potential due to both charges

Vi = 9*10^9 * 83.23 *10^-3/.3164 + 9*10^9 * 28.91 *10^-3/sqrt(0.3515^2 + 0.3164^2)

Vi = 2.918 *10^9 V

at point A

VA = 9*10^9 * 28.91 *10^-3/.1055 + 9*10^9 * 83.23 *10^-3/(0.3515 - 0.1055)

VA = 5.511 *10^9 V

Now , let the speed of third is v m/s at A

change in kinetic energy = decrease in potential energy

0.5 * 0.04131* v^2 = 7.051 *10^-6 * (5.511 *10^9 - 2.918 *10^9 )

solving for v

v = 940.8 m/s

the speed of third particle at A is 940.8 m/s

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