A small metal sphere, carrying a net charge of q_1 = -2.90 mu C is held in a sta

Question

A small metal sphere, carrying a net charge of q_1 = -2.90 mu C is held in a stationary position by insulating supports. A second small metal sphere, with a net charge of q_2 = -7.70 mu C and mass 1.50 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 (Figure 1). 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 0.380 m apart? How close does q_2 get to q_1?

Explanation / Answer

in both the cases, we have to conserve the total energy.

q1 = -2.9 uC

q2 = -7.7 uC

m = 1.5 x 10-3 kg

d = 0.8 m

vi = 22 m/s

r1 = 0.380 m

A) kq1q2/d + mvi2/2 = kq1q2/r1 + mv2/2

=> [9 x 109 x (-2.9 x 10-6) x (-7.7 x 10-6) x (1/0.8 - 1/0.38)] x 2/(1.5 x 10-3) = v2 - 222

=> v = 10.66 m/s

B) for minimum distance, v = 0

kq1q2/d + mvi2/2 = kq1q2/r

=> 1/d + (mvi2/2)/kq1q2 = 1/r

=> 1/0.8 + (1.5 x 10-3 x 222/2)/(9 x 109 x (-2.9 x 10-6) x (-7.7 x 10-6)) = 1/r

=> r = 0.3272 m

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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