Step 1: Understanding the Concept:
Coulomb's Law provides the mathematical description of the electrostatic force between two stationary, electrically charged particles.
The law states that the force (\(F\)) is directly proportional to the product of the magnitudes of the charges (\(q_1\) and \(q_2\)) and inversely proportional to the square of the distance (\(r\)) between them.
This is an "Inverse Square Law," similar in form to Newton's law of universal gravitation.
Key Formula or Approach:
\[ F = \frac{k |q_1 q_2|}{r^2} \]
Where:
\(k\) = Coulomb's constant \(\approx 9 \times 10^9 \text{ N}\cdot\text{m}^2/\text{C}^2\).
\(q_1, q_2\) = charges in Coulombs (C).
\(r\) = distance in meters (m).
Step 2: Detailed Explanation:
Let's convert our units to SI before calculating:
\(q_1 = 2 \mu C = 2 \times 10^{-6}\) C.
\(q_2 = 8 \mu C = 8 \times 10^{-6}\) C.
\(r = 2\) m.
Now, substitute these into the Coulomb's Law formula:
\[ F = \frac{(9 \times 10^9) \times (2 \times 10^{-6}) \times (8 \times 10^{-6})}{(2)^2} \]
Simplify the powers of 10:
\[ F = \frac{9 \times 2 \times 8 \times 10^{(9 - 6 - 6)}}{4} \]
\[ F = \frac{144 \times 10^{-3}}{4} \]
Dividing 144 by 4 gives 36:
\[ F = 36 \times 10^{-3} \text{ N} \]
Converting from scientific notation to standard decimal format:
\[ F = 0.036 \text{ N} \]
This force is repulsive because both charges have the same (positive) sign.
Step 3: Final Answer:
The force is 0.036 N, which matches option (B).