A small metal sphere, carrying a net charge of q 1 = ?2.80 C, is held in a stati

Question

A small metal sphere, carrying a net charge of q1 = ?2.80 C, is held in a stationary position by insulating supports. A second small metal sphere, with a net charge of q2 = ?3.60 C and mass 1.60 g, is projected toward q1. When the two spheres are 0.800 m apart, q2 is moving toward q1 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 q2 when the spheres are 0.400 m apart?
_________m/s

(b) How close does get q2 to q1?
_________m

Explanation / Answer

Solution:

a) The solution to this problem is based on the conservation of energy.

Since the charge has a velocity v = 22 m/s initially at the distance 0.8m,

it has kinetic energy as well as electrostatic potential energy .

Total energy = E1 =Initial kinetic energy + electrostatic potential energy = KEi = 1/2 m v^2 + k q1q2/r

                                                                                      = 1/2 * (1.6 e-3)(22)^2 + (9 e9)(2.8 e-6)(3.6 e-6)/0.8

                                                                                     = 0.3872 + 0.1134

                                                                                      = 0.5 j

Final energy = 1/2mv2^2 + kq1q2/r2 = 0.5 * (1.6 e-3) v2^2 + [(9 e9)(2.8 e-6)(3.6 e-6)] / 0.4

                                                           = 8 e-4 v2^2 + 0.2268

Ei = Ef

=> 0.5 = 8 e-4 v2^2 + 0.2268

=> 8 e-4 v2^2 = 0.5 - 0.2268

                     = 0.27

=> v2 ^2 = 0.27 /(8 e-4)

=> v2 = 18.4 m/s

b) At the closest distance velocity =0 ; so kinetic energy =0

Ei= Electrostatic potential energy

=> 0.5 = (9 e9)(2.8 e-6)(3.6 e-6)/r

=> r = (9 e9)(2.8 e-6)(3.6 e-6) /0.5

         = 0.18 m

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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