# Coulomb's formula - doubt

1. Mar 10, 2009

### nikromancer

Coulomb's formula states that the force of attraction between two electrically charged bodies is k(q1*q2/d^2), where k is 9*10^9 Nm^2/C^2. However, I have a doubt regarding this.
We know that like charges repel and unlike charges attract. Let us take the case of like charges first. If both q1 and q2 are like charges, the value of q1*q2 will be positive. As d and k are also positive, the force of attraction will also be positive. However, this means that like charges ATTRACT each other rather than repel. Similarly, if q1 and q2 are unlike charges, then the force of attraction will be negative and this means that unlike charges repel and like charges attract. But this isn't true.
So, shouldn't the formula be F= -k(q1*q2/d^2) or |F|=k(|q1*q2|/d^2)?? Please clarify.

2. Mar 10, 2009

### CompuChip

The formula you give only gives the magnitude of the force, not the direction.

The full (vector) form giving the force on charge 1 is
$$k {q_1q_2 \over r^2}\mathbf{\hat{r}}_{21}$$
where $\mathbf{\hat{r}}_{21}$ is the vector pointing from charge 2 to charge 1. So if the charges are like, then the force vector will point along this vector, meaning it is repulsive.

3. Mar 10, 2009

### Galileo

You shouldn't interpret F as the force of attraction. The F in Coulomb's law is simply THE force charge 1 exerts on charge 2. If it is negative, it will be attractive (in the direction to make the distance between chages decrease) and if it is positive, it will be repulsive.

The notation you are using can confuse whether the force is attractive or not. The unambiguous way of writing coulomb's law is with vector notation (3 dimensions):

The force charge 1 exerts on charge 2 is

$$\vec F = K \frac{q_1q_2}{r^2}\hat r$$
where $\hat r$ is the unit vector from q1 to q2 (i.e. $\vec r_2-\vec r_1$).

In one dimension, you can work with signs, but you have to take care with the directions.

F = K(q_1q_2/d^3) * (x2-x1), where (x2-x1) is the signed distance x2-x1. So if x2>x1, then x2-x_1=d and the force is Kq_1q_2/d^2. This is positive for like charges, to the force is such that x_2 tends to increase (repellant). Figure out the other cases yourself.