Q. 22

# Two identical bal

Answer :

Given,

Mass,

Length of strings, l = 50cm = 0.5 m

Distance between spheres,

Magnitude of charge on each ball,

Let the magnitude of Tension be T. Let the magnitude of electric force between the spheres be F_{e}.

Note that tension will adjust itself so that there is no acceleration along its direction.

(a)

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**Formula used:**

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

Where ϵ_{0} is the permittivity of free space

q_{1} and q_{2} 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, F_{e} is given by:

Hence, the electric force is 0.144 N along the line joining the charges and away from the other charge.

(b)

By trigonometry,

Now, along the string, there is component of acceleration. Hence,

Now, consider the direction perpendicular to the string,

Hence, the component of net force perpendicular to the string is 0.095N and away from the other charge (indicated by positive sign)

(c)From the free body diagram,

Rearranging to get the above expression, we get

(d)

Applying Newton’s second law along the y-direction,

Thus the acceleration of one of the balls is 0.95ms^{2} perpendicular to the string and going away from the other charge.

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