A small ball of mass, m = 7.60 × 10-12 kg, has acquired an excess charge. The ba
ID: 251822 • Letter: A
Question
A small ball of mass, m = 7.60 × 10-12 kg, has acquired an excess charge. The ball is then placed between two parallel plates spaced x = 0.00315 m which have a potential difference of V = 1860 V applied across them. In this configuration the ball appears to be motionless or floating in between the plates. What is the overall charge on the ball? Calculate the number of electrons, ne, the ball has either gained or lost. The acceleration due to gravity is g = 9.81 m/s2, and the elementary unit of charge is e = 1.60 × 10-19 C.
Explanation / Answer
given data
as the ball is inside the plates of capacitors the force acting on the charged ball can be written as
electric force = gravitational force
we know that v= E*d => E = V/d, F= Eq = mg,
V/d*n*q = mg
n = mg*d/V
= 7.6*10^-12*9.81*0.00315/ 1860
= 789.151
the number of electrons gained by ball is 789.151 times the elementary charge.
in this case the ball will be in equilibrium, means motionless when it gains 789.151*q charge.
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