Two small spheres each of mass 10 mg are suspended from a point by threads 0.5m long. They are equally charged and repel each other to distance of 0.28m. If g=10m/s^2, what is charge on each?

Question

Answer

Answer

Calculation of Charge on Small Spheres

Given Data:

Mass of each sphere = 10 mg = 10 x 10^-6 kg

Length of thread = 0.5 m

Distance between spheres = 0.28 m

Acceleration due to gravity (g) = 10 m/s^2

Calculation:

Let q be the charge on each sphere.

Since the spheres repel each other, the electrostatic force between them is given by Coulomb's law:

F = k * (q^2) / r^2

The gravitational force on each sphere is given by:

F = m * g

Since the spheres are in equilibrium, the electrostatic force must be equal and opposite to the gravitational force:

k * (q^2) / r^2 = m * g

Substituting the given values, we get:

k * (q^2) / (0.28)^2 = 10 * 10^-6 * 10

Rearranging and solving for q, we get:

q = sqrt((0.28)^2 * 10 * 10^-6 * 10 / k)

Substituting the value of Coulomb's constant k, we get:

q = sqrt((0.28)^2 * 10 * 10^-6 * 10 / (9 x 10^9))

Simplifying, we get:

q = 2.97 x 10^-7 C

Conclusion:

The charge on each small sphere is 2.97 x 10^-7 C.

Answer

Charge=2.4×10^6 Coulmb

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