Two small conducting point charges, separated by 0.5 m, carry a total charge of 170 mu or micro CC. They repel one another with a force of 120 N. For the universal constant k use the value 8.99 times 109 N m2/C2.
Find the charge on the larger of the two point charges.
Question
Answer:
the two point charges are equal
q₁ = 147.353 x 10⁻⁶ C or 22.646 x 10⁻⁶ C
q₂ = 22.647 x 10⁻⁶ C or 147.354 x 10⁻⁶ C
Explanation:
Given;
distance between the two charges, r = 0.5 m
let the first charge = q₁
let the second charge = q₂
q₁ + q₂ = 170μ = 170 x 10⁻⁶ C ———- equation (1)
Force of repulsion between the two charges, q₁ and q₂ = 120 N
Coulomb’s constant, K = 8.99 x 10⁹ N m²/C²
Apply coulomb’s law, for force of attraction or repulsion between two point charges;
From equation (1); q₂ = 170 x 10⁻⁶ C – q₁
Substitute in the value of q₂ in equation (2)
q₁(170 x 10⁻⁶ – q₁) = 3.337 x 10⁻⁹
170 x 10⁻⁶q₁ – q₁² = 3.337 x 10⁻⁹
170 x 10⁻⁶q₁ = q₁² + 3.337 x 10⁻⁹
0 = q₁² – 170 x 10⁻⁶q₁ + 3.337 x 10⁻⁹ (this is quadratic equation)
q₁ = 147.353 x 10⁻⁶ C or 22.646 x 10⁻⁶ C
q₂ = 170 x 10⁻⁶ C – q₁
q₂ = 170 x 10⁻⁶ C – 147.353 x 10⁻⁶ C or 170 x 10⁻⁶ C – 22.646 x 10⁻⁶ C
q₂ = 22.647 x 10⁻⁶ C or 147.354 x 10⁻⁶ C
Therefore, the two point charges are equal