This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Step 1: The electrostatic force between two point charges q_1 and q_2 separated by a fixed distance r is given by F = (k |q_1 q_2|)/(r^2) where k is Coulomb's constant. Here, q_1 + q_2 = 4\, and r is fixed, so F |q_1 q_2|. Step 2: Let q_1 = q\, and q_2 = (4 - q)\,. Then, the product is P = |q(4 - q)|\,^2 = |4q - q^2|\,^2. Since 0 ≤ q ≤ 4, P = 4q - q^2. Step 3: To maximize P, take the derivative: (dP)/(dq) = 4 - 2q. Set (dP)/(dq) = 0: 4 - 2q = 0 q = 2. Step 4: Second derivative test: (d^2P)/(dq^2) = -2 < 0, so maximum at q = 2\,. Step 5: Verify with options (products in ^2): (a) 1 × 3 = 3 (b) 2 × 2 = 4 (maximum) (c) 0 × 4 = 0 (d) 1.5 × 2.5 = 3.75 (b) 2 μC और 2 μC