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 = -4.00 mu C and mass 2.10 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. (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 uC = - 2.8 * 10^-6 C

q2 = - 4 uC = -4 * 10^-6 C

m2 = 2.1 g = 0.0021 kg

r1 = 0.8 m

r2 = 0.4 m

intial speed , u = 22 m/s

a)

let the speed of q2 when spheres are 0.4 m apart be v

using conservation of energy

kinetic energy lost = potential energy gained

0.5 * m2 * ( u^2 - v^2) = k * q1 * q2 * ( 1/r2 - 1/r1)

0.5 * 0.0021 * ( 22^2 - v^2) = 9 * 10^9 * 2.8 * 10^-6 * 4 * 10^-6 * ( 1/0.4 - 1/0.8)

v = 19.1 m/s

b)

let the minimum distance between q1 and q2 be r

using conservation of energy

kinetic energy lost = potential energy gained

0.5 * m2 * ( u^2 - v^2) = k * q1 * q2 * ( 1/r - 1/r2)

0.5 * 0.0021 * ( 22^2 - 0^2) = 9 * 10^9 * 2.8 * 10^-6 * 4 * 10^-6 * ( 1/r - 1/0.8)

r = 0.16 m

the minimum distance is 0.16 m

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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