Wo identical 7.10-gg metal spheres (small enough to be treated as particles) are hung from separate 700- strings attached to the same nail in a ceiling. Surplus electrons are added to each sphere, and then the spheres are brought in contact with each other and released. Their equilibrium position is such that each string makes a 17.0 ∘∘ angle with the vertical.

How many surplus electrons are on each sphere?

Explanation:

Using the expression of electric force:

and replacing mgtanθ for F , q for and d for r in the relation above:

Then;

making a the subject of the formula ; we have:

   -------------- equation (1)

By trigonometric rule:

let be the opposite side; and

l be the adjacent side in the above equation and solve for d:

Then

Replacing into equation  1 ; we have:

Equation for number of charge particle n =

So;

Given that :

m = 7.10 g

θ = 17.0 °

g = 9.80 m/s²

k = 8.99× 10 ⁹ N.m ²/C²

l = 700 mm

e = 1.6× 10⁻¹⁰

Then;

Therefore ; the number of surplus electron that are on each sphere =

The number of electrons are 3.94x10¹²

Explanation:

The translational equilibrium is:

Dividing the expression by Tcosθ = mg

The equation for electric force is:

if:

Replacing:

Where

L = 700 mm = 0.7 m

ε = 1.6x10⁻¹⁹C

m = 7.1 g = 0.0071 kg

k = 8.99x10⁹N m²/C²

Replacing:

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