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:

r=rho l/a where a is the area, l is the length and rho is resistivity so the greater the area the lesser the resistance thats why the earth pin is thicker bcos current follow the shortest path, so less resistive .