# Homework Help: Coulomb's law and related problem

1. Jul 12, 2011

### logearav

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

3. 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+6x10-6q2-16x10-12=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
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Jul 12, 2011

### Staff: Mentor

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.
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 $q_2 = Q - q_1$

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

3. Jul 12, 2011

### logearav

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

4. Jul 12, 2011

### Staff: Mentor

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

5. Jul 13, 2011

### 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 whats wrong with my assumption?

6. Jul 13, 2011

### Staff: Mentor

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

7. Jul 13, 2011

### logearav

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