A charged polystyrene ball of mass 0.14g is suspended by a nylon thread from a fine glass spring.  In the absence of any electric field the spring extends by 30mm.  The polystyrene ball is then placed in an electric field that acts vertically upwards, of strength 2.0 x 105 Vm-1, and the spring extends by a further 6.0mm.  What is the electric charge on the polystyrene ball?

Expert Answers

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When the charged polystyrene ball of mass 0.14 g is suspended by a nylon thread from a fine glass spring in the absence of any electric field, the spring extends by 30 mm.

If the spring constant of the glass spring is k, `0.14*10^-3*9.8 = k*30*10^-3`

=> `k = (0.14*9.8)/30 = 343/7500`

When there is an electric field of strength `2*10^5 V/m` acting vertically upwards, the spring is extended further by `6*10^-3` m.

If the ball has a charge X C, the force due to the field is 2*10^5*X

`2*10^5*X = (343/7500)*(6/1000)`

=> `X = 1.372*10^-9 C`

The electric charge on the polystyrene ball is `1.372*10^-9` C

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