A small metal sphere has a mass of 0.19g and a charge of -27.0nC . It is 10 cm d

Question

A small metal sphere has a mass of 0.19g and a charge of -27.0nC . It is 10 cm directly above an identical sphere with the same charge. This lower sphere is fixed and cannot move.

Part A

What is the magnitude of the force between the spheres?

Express your answer to two significant figures and include the appropriate units.

Part B

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.

Explanation / Answer

Its given that,

mass of the sphere = m1 =m2 = 0.19g = 0.00019 kg and charge = q1 =q2 = -27 nC = -2.7 x 10-8 C

(same for both the spheres)

Dist. between the spheres = r = 10 cm = 0.1 m

Part (A) We know that, the eletcricforce of attraction or replusion between the charged particle is given by :

F(elect) = K q1 q2 / r2 where K = 8.98 x 109 N m2/C2

F = 8.98 x 109 N m2/C2 (-2.7 x 10-8 C)2 / (0.1)2

F(elect) = 6488.1 x 10-7 N = 6.49 x 10-4 N

Part (B)

both the spheres carry same charges , so the electric force between them will be repulsive and when the sphere will be allowed to fall, the electric force of repulsion will be oppsing it. So net force on the falling charged sphere wil be

F(net) = m g - f (elect)

F(net) = 0.00019 kg x 9.8 - 6.488 x 10-4 N = 0.0012132 N

We also know that, F(net) = ma

a = F(net) / m = 0.0012132 N / 0.00019 kg = 6.39 m/s2

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