Is Coulomb's law consistent with Newton's Third Law? In particular, how do
F^elec A-->B and F^elec B--->A compare in magnitude? in direction?
they are the same magnitude and opposite in direction like any other forces
To determine if Coulomb's law is consistent with Newton's Third Law, we need to analyze the relationship between the electrostatic forces exerted by two charged particles on each other.
Coulomb's law states that the magnitude of the electrostatic force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. Mathematically, it is represented as:
F^elec = (k * |q1 * q2|) / r^2
where F^elec is the electrostatic force, k is the electrostatic constant, q1 and q2 are the charges of the particles, and r is the distance between them.
Newton's Third Law states that for every action, there is an equal and opposite reaction. This means that if one charged particle (A) exerts a force on another (B), the second particle (B) will also exert an equal but opposite force on the first (A).
Therefore, when considering Coulomb's law and Newton's Third Law together:
1. Magnitude: The magnitudes of the electrostatic forces, F^elec A-->B and F^elec B--->A, will be equal in magnitude. This is because Coulomb's law states that the force between two charges is proportional to the product of their charges, which means that the magnitude of the force will be the same regardless of which charge is considered as the source or the target.
2. Direction: Coulomb's law tells us that the electrostatic force is along the line joining the charges. When considering Newton's Third Law, the direction of F^elec A-->B is from A to B, while the direction of F^elec B--->A is from B to A. Therefore, the forces will have opposite directions but equal magnitudes.
In summary, Coulomb's law is consistent with Newton's Third Law. The magnitude of the electrostatic forces exerted by two charged particles on each other will be equal, while the direction of the forces will be opposite.