Question^ A small metal sphere, carrying a net charge of q1 = -3.08muC , is held

Question

Question^

A small metal sphere, carrying a net charge of q1 = -3.08muC , is held in a stationary position by insulating supports. A second small metal sphere, with a net charge of q2 = -6.07muC and mass 1.51g, is projected toward q1. When the two spheres are 0.800 m apart, q2 is moving toward q1 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 q2 when the spheres are 0.321m apart? How close does q2 get to ql?

Explanation / Answer

U1 = energy of q2 at when sepration is 0.8 m

      = potentail energy + kinetic energy

      = k*q1*q2/0.8 + mv^2/2

      = k*q1*q2/0.8 + m*22^2/2

where k =9*10^9

U2 = energy of q2 at when sepration is 0.32 m

      = k*q1*q2/0.32 + m*V^2/2

from conservation of energy :::

U2 =U1

k*q1*q2/0.32 + m*V^2/2    =   k*q1*q2/0.8 + m*22^2/2

                          V^2       =(2*k*q1*q2/m)( 1/0.8 -1/0.32) + 22^2

                                       =(2*9*10^9*3.08*6.07*10^-12/0.001.5)( 1/0.8 -1/0.32) +22^2

                                      = -224.3 *1.875 + 22^2

                                      = 63.43

                           V = 7.96 m/s

b) let q2 is at a distance r from q1 ::

       U3 = energy of q2 at r

              = k*q1*q2/r

from coservation of energy ::

    U3 = U1

   k*q1*q2/r    = k*q1*q2/0.8 + m*22^2/2

         1/r          = 1/0.8     + m*22^2/(2*k*q1*q2)

                        = 1/0.8     + 1.5*22^2*10^-3/( 2*9*10^9*3.08*6.07*10^-12)

                         =1/0.8   + 1.5*22^2/( 2*9*3.08*6.07)

                        = 3.40

              r =1/3.40 = 0.29 m

       

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