Answer :
Explanation:
Hey there! Coulomb's law in vector form states that the electrostatic force between two point charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. Mathematically, it can be expressed as:
F = k * (q1 * q2) / r^2 * r̂
where:
- F is the electrostatic force vector,
- k is Coulomb's constant,
- q1 and q2 are the magnitudes of the charges,
- r is the distance between the charges,
- r̂ is the unit vector pointing from charge q1 to charge q2.
Now, to prove that Fvector 21 = -Fvector 12, let's consider two charges q1 and q2. The force on q2 due to q1 (Fvector 21) is given by:
Fvector 21 = k * (q1 * q2) / r^2 * r̂21
where r̂21 is the unit vector pointing from q1 to q2.
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Similarly, the force on q1 due to q2 (Fvector 12) is:
Fvector 12 = k * (q1 * q2) / r^2 * r̂12
Now, since r̂21 = -r̂12 (opposite directions), we can see that:
Fvector 21 = -Fvector 12
This result shows that the forces on the two charges are equal in magnitude but opposite in direction, which is a consequence of Newton's third law of motion.