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.

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;

--------------  equation (2)

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

force required to detach it is given by

charges are taken to be fundamental charge

now we have

so above is the minimum distance at which it will detach