Coulomb's law and related problem

[logearav]

Homework Statement

The sum of two point charges is 6µC. They attract each other with a force of 0.9 N, when kept 40 cm apart in vacuum. Calculate the charges.

Homework Equations

The Attempt at a Solution

q₁+(-q₂) = 6x10^-6
q₁-q₂=6x10^-6...I
q₁=6x10^-6+q₂
According to Coulomb's law
F=q₁q₂/4πε₀r²
.9=(6x10^-6+q₂)q₂/4πε₀(.4)²
.9=(6x10^-6q₂+q₂²)x9x10⁹/.16
.144/9x10⁹=6x10^-6q₂+q2²
144x10^-3x10^-9/9=6x10^-6q₂+q₂²
q₂²+6x10^-6q_2-16x10^-12=0
(q₂+8x10^-6)(q₂-6x10^-6)=0
q₂₌-8µC or q₂=6µC
The answers given in the book are q₁ = 8micro Coulomb and q₂= -2 microcoulomb
I don't understand how to get this answer because when q₂ = 8 microcoulomb and substituting in equation I , i get q₁+8micro coulomb =6 micro coulomb so q₁ should be -2 micro coulomb
Did i miss anything in the steps? Members, please help me .

 

[gneill]

The Attempt at a Solution

q₁+(-q₂) = 6x10^-6
q₁-q₂=6x10^-6...I
q₁=6x10^-6+q₂

Since you're assuming that q₁ is positive and that q₂ is negative, you don't need to wedge in that extra minus sign. Just write q₁ + q₂ = 6x10^-6C.

According to Coulomb's law
F=q₁q₂/4πε₀r²
.9=(6x10^-6+q₂)q₂/4πε₀(.4)²

Since one of the charges is negative the product q₁*q₂ will be negative, and thus the force should be negative also.

Let f = 0.9N, r = 0.40m, Q = 6μC, $k = \frac{1}{4 \pi \epsilon_o}$ Then

$Q = q_1 + q_2$ so that $q_2 = Q - q_1$

$f = -k \frac{q_1 q_2}{r^2} = -k \frac{q_1 (Q - q_1)}{r^2}$

 

[logearav]

it has been mentioned that two charges attract each other that's why i took q2 as negative. is my assumption wrong, sir?

 

[gneill]

it has been mentioned that two charges attract each other that's why i took q2 as negative. is my assumption wrong, sir?

No, the assumption is fine. Oppositely signed charges attract. Either q1 or q2 must be negative (but not both!).

 

[logearav]

Thanks a lot for the reply, sir. Then why i didn't get the correct answer when i framed the equation q1-q2= 6 micro coulomb, taking q1 as positive and q2 is negative. I got the correct answer when i proceeded as suggested by you. But what's wrong with my assumption?

 

[gneill]

Thanks a lot for the reply, sir. Then why i didn't get the correct answer when i framed the equation q1-q2= 6 micro coulomb, taking q1 as positive and q2 is negative. I got the correct answer when i proceeded as suggested by you. But what's wrong with my assumption?

q1 - q2 is the difference between the charges, not the sum of the charges.

 

[logearav]

I got it sir. Thanks a lot for patiently helping me.