if the force vector F elect A-->B is in the positive direction form the unit vector r A-->B , the unit vector must be multiplied by a negative number . where does this negative number come from in the Coulomb equation? Does this negative number indicate a repulsive force or an attractive force?
In the Coulomb equation, the negative sign is present to indicate the nature of the force. It represents an attractive force between charged particles.
To understand where this negative sign comes from, let's review the Coulomb equation. The Coulomb equation states that the force between two charged particles is given by:
F = k * (q1 * q2) / r^2
Here:
- F is the force between the charges q1 and q2.
- k is the Coulomb's constant, which is a positive value.
- r is the distance between the charges.
When calculating the direction of the force, we use a unit vector pointing from one charge to the other (let's call it r A-->B ). By convention, the force vector F is taken to point in the same direction as the unit vector r A-->B .
However, the force felt by one charge due to the other is attractive if the charges have opposite signs. This implies that the force vector and the unit vector have opposite directions.
To incorporate this directionality, we introduce a negative sign in the Coulomb equation if the charges have opposite signs. This negative sign ensures that the force vector points in the opposite direction to the unit vector, indicating an attractive force.
Therefore, the negative sign in the Coulomb equation is necessary to differentiate between attractive and repulsive forces, with an attractive force indicated by the negative sign.