Two small plastic spheres are given positive electrical charges. When they are 16.0 cm apart, the repulsive force between them has magnitude 0.200 N . Part A What is the charge on each sphere if the two charges are equal

q = 7.542 x 10⁻⁷ C = 754.2 nC

Explanation:

The Coulomb's Law gives the magnitude of the force of attraction or repulsion between two charges:

F = kq₁q₂/r²

where,

F = Force of attraction or repulsion = 0.2 N

k = Coulomb's Constant = 9 x 10⁹ N m²/C²

r = distance between charges = 16 cm = 0.16 m

q₁ = magnitude of 1st charge

q₂ = magnitude of 2nd charge

Since, both charges are said to be equal here.

q₁ = q₂ = q

Therefore,

0.2 N = (9 x 10⁹ N m²/C²)q²/(0.16 m)²

(0.2 N)(0.16 m)²/(9 x 10⁹ N m²/C²) = q²

q = √(5.88 x 10⁻¹³ C²)

q = 7.542 x 10⁻⁷ C = 754.2 nC