Two point charges have a total charge of 253 μC . When placed 1.71 m apart, the force each exerts on the other is 17.1 N and is repulsive.?

Question

What is the charge on each?

Answer 1

I will show you how to work this problem, and you do the calculations.

 

F = kq₁q₂/r²

 

F = 17.1 N

k = 9 x 10⁹ Nm²/C²

r = 1.71 m

q₁ + q₂ = 253 x 10^-6 C 

 

q₁q₂ = Fr²/k = (17.1)(1.71)²/(9 x 10⁹) C² ≅ 5.556 x 10^-9 C² 

 

Solve for q₁ and q₂ from

 

q₁ + q₂ = 253 x 10^-6 C

q₁q₂ = 5.556 x 10^-9 C²

 

At this point, you have just 2 equations in 2 unknowns q₁ and q₂.  Solve the system of equations, and remember that for the force to be repulsive, both charges are positive, or both charges are negative.  Since the sum of the charges was given as positive, assume both charges are positive when you solve.  You should be able to finish from here.