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How many electrons must be removed from each of the two spheres so that the force of electrostatic repulsion exactly balances the gravitational attraction?

User Emad Adly
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Answer / Explanation:

For proper clarity, let us recall Coulomb's Law,

Where, m = mass of an electron = 9.1 x 10⁻³¹

q = The electric charge of the electron = 1.6 x 10 ⁻¹⁹

r = The distance between the two electrons

G = Universal gravitational constant = 6.67 x 10⁻¹¹Nm²/Kg²

K = 8.9 x 10 ⁹ Nm²/C²

Now, considering the fact that the number of electron removed from the spheres was not given,

We assume this to be = "n"

Where the electric charge of the electron = 1.6 x 10 ⁻¹⁹ . n (where n = number of electron removed from each sphere)

Since we were not given the mass of the sphere, we try to calculate it from the volume using the formula:

V = 4/3πr³,

However, from coulombs law, mass of the electron = 9.1 x 10⁻³¹

Consequentially, where electrostatic repulsion = gravitational attraction

Therefore, recalling the formula,

Kq₁ q₂ / R² = Gмm / R²

Now inserting the value from the constant stated initially,

we have,

(8.9 x 10 ⁹)(1.6 x 10 ⁻¹⁹n)(1.6 x 10 ⁻¹⁹n)/R² = (6.67 x 10⁻¹¹)(9.1 x 10⁻³¹)/R₂

Doing a proper calculation of the above,

we should get n = 6.805838 × 10⁶

The answer is 6.805838 × 10⁶

User IgorL
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