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 comes from the fact that the electric force between two charged particles is an attractive force for opposite charges and a repulsive force for like charges. The negative sign indicates the attractive or repulsive nature of the force.
To understand why the negative sign is used in the Coulomb equation, let's consider two charged particles with charges q1 and q2, located at positions r1 and r2, respectively. The electric force vector F on q2 due to q1 is given by Coulomb's law equation:
F = (1 / 4πε₀) * (q1 * q2 / r^2) * r̂
In this equation, ε₀ is the permittivity of free space, r is the distance between the charges, and r̂ is the unit vector pointing from q1 to q2.
The negative sign is applied when we take into account the repulsive or attractive nature of the force. If q1 and q2 have opposite charges (one positive and one negative), the force between them is attractive, and the negative sign is not necessary. However, if q1 and q2 have the same charges (both positive or both negative), the force between them is repulsive, and we need to include the negative sign in the equation.
To summarize, if the force vector F and the unit vector r̂ have the same direction, the negative sign is not needed in the Coulomb equation because the charges have opposite signs and it represents an attractive force. If the force vector F and the unit vector r̂ have opposite directions, we include the negative sign because the charges have the same sign and it represents a repulsive force.