# A charged polystyrene ball of mass 0.14g is suspended by a nylon thread from a fine glass string. In the absence of any electric field the spring extends by 30mm. The polystyrene ball is then...

A charged polystyrene ball of mass 0.14g is suspended by a nylon thread from a fine glass string. 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 2.0x10^5Vm^-1, and the spring extends by a further 6.0mm. What is the electric charge on the polystyrene ball? (Help get to the solution please)

llltkl | College Teacher | (Level 3) Valedictorian

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

So, by Hooke's law:

`F=kx` where k is the spring constant

`rArr mg=kx`

`rArr 0.14*10^-3*9.8=k*30*10^-3`

`rArr k=(0.14*9.8)/30=0.045733`

Again, when the polystyrene ball is placed in an electric field that acts vertically upwards, of strength 2.0x10^5 Vm^-1, the spring extends and reaches an equilibrium by etending a further 6.0 mm.

Let the the electric charge on the polystyrene ball be `X` . The force acting on the ball due to the applied electric field is given by:

F=E*c

At equilibrium, `2.0*10^5*X=0.045733*6*10^-3`

`rArr X=(0.045733*6*10^-3)/(2.0*10^5)`

`rArr X=1.37*10^-9` ` C`