# Coulomb's law and related problem

• logearav
In summary, the sum of two point charges is 6µC, and they attract each other with a force of 0.9 N when kept 40 cm apart in vacuum. To calculate the charges, one must use Coulomb's law and the equation q1 + q2 = 6x10^-6C. One of the charges must be negative, and the correct answers are q1 = 8 microcoulomb and q2= -2 microcoulomb.
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.

## 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

logearav said:

## 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 $q_2 = Q - q_1$

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

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

logearav said:
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!).

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?

logearav said:
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.

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

## 1. What is Coulomb's Law?

Coulomb's Law is a fundamental law of physics that describes the force between two charged particles. It states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

## 2. How is Coulomb's Law related to electrostatics?

Coulomb's Law is the foundation of electrostatics, which is the study of stationary electric charges. It explains how electric charges interact with each other and the resulting forces between them.

## 3. What is the SI unit for electric charge?

The SI unit for electric charge is the coulomb (C). It is defined as the amount of charge that passes through a conductor in one second when a current of one ampere is flowing.

## 4. How does the distance between two charged particles affect the force between them?

According to Coulomb's Law, the force between two charged particles is inversely proportional to the square of the distance between them. This means that as the distance between the particles increases, the force decreases.

## 5. Can Coulomb's Law be used for both positive and negative charges?

Yes, Coulomb's Law applies to both positive and negative charges. The only difference is that like charges (both positive or both negative) repel each other, while opposite charges (positive and negative) attract each other.

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