A small metal sphere has a mass of 019 g and a charge of 210

A small metal sphere has a mass of 0.19 g and a charge of -21.0 nC. It is 10 cm directly above an identical sphere with the same charge. This lower sphere is fixed and cannot move. What is the magnitude of the force between the spheres? Express your answer to two significant figures and include the appropriate units. If the upper sphere is released, it will begin to fall. What is the magnitude of its initial acceleration? Express your answer to two significant figures and include the appropriate units.

Solution

mass of the sphere m = 0.19 g = 0.19 x10 ^-3 kg

Separation of the two spheres r =10 cm = 0.1 m

Charge of the sphere q = -21 nC = -21 x10 ^-9 C

(a). Magnitude of the force between the two spheres F = Kqq / r ²

Where K = Coulomb\'s constant = 8.99 x10 ⁹ Nm ²/ C ²

Substitute values you get F = (8.99 x10 ⁹) (21 x10 ^-9)(21 x10 ^-9 ) / 0.1 ²

                                        = 3.96459 x10 ^-4 N

                                        = 4.0 x10 ^-4 N            ( two significant figures)

This force is repulsive.i.e., it cat upward on upper charged sphere.

(b). Weight of the upper sphere W = mg

                                                  = 0.19 x10 ^-3 x 9.8

                                                  = 1.862 x10 ^-3 N

Net force on upper sphere F \' = W - F

                                          = (1.862 x10 ^-3 ) -(3.96459 x10 ^-4 )

                                          = 1.4655 x10 ^-3 N

Magnitude of initial accleration a = F \' / m

                                                =(1.4655 x10 ^-3 ) / (0.19 x10 ^-3 )

                                                = 7.713 m/s ²

                                                = 7.7 m/s ²      ( two significant figures)