# Two small spheres, each having a mass of 20g, are suspended from a common point by two insulating strings of length 40 cm each. The spheres are identically charged and the separation between the balls at equilibrium is found to be 4 cm. find the charge on each sphere.

Given,

Mass,

Length of strings, l = 40cm = 0.4 m

Distance between spheres,

Let the magnitude of Tension be T. Let the electric force between the spheres be Fe. Let the magnitude of charge on each pitch ball be q.

By trigonometry,

At equilibrium, all forces must cancel out in accordance with newton’s first law. Hence,

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Formula used:

By Coulomb’s law, the electric force is given by:

Where ϵ0 is the permittivity of free space

q1 and q2 are the magnitude of charges

r is the distance of separation between the charges

(Here, )

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The magnitude of the electric force, Fe is given by:

From (2), we get,

From (3) and (1), we get

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