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: Identify the given values for part (a). The charges on the spheres are q_1 = q_2 = 6.5 × 10^-7 C. The distance between the spheres is r = 50 cm = 0.50 m. The electrostatic constant is k = (1)/(4_0) = 9 × 10^9 N m^2/C^2. Step 2: Calculate the electrostatic force for part (a) using Coulomb's Law. The formula for Coulomb's Law is F = k (q_1 q_2)/(r^2). F = (9 × 10^9 N m^2/C^2) (6.5 × 10^-7 C) × (6.5 × 10^-7 C)(0.50 m)^2 F = (9 × 10^9) 42.25 × 10^-140.25 N F = (9 × 10^9) × (169 × 10^-14) N F = 1521 × 10^-5 N F = 1.521 × 10^-2 N Rounding to two decimal places for the coefficient: F = 1.52 × 10^-2 N Step 3: Identify the new conditions for part (b). The new charges are q_1' = 2q_1 and q_2' = 2q_2. The new distance is r' = (r)/(2). Step 4: Calculate the new electrostatic force for part (b). The new force F' is given by: F' = k (q_1' q_2')/((r')^2) Substitute the new values: F' = k ((2q_1)(2q_2))/((r)2)^2 F' = k (4q_1 q_2)/(r^2)4 F' = 16 ( k (q_1 q_2)/(r^2) ) Since F = k (q_1 q_2)/(r^2), we have F' = 16F. Step 5: Substitute the value of F from part (a) into the expression for F'. F' = 16 × (1.52 × 10^-2 N) F' = 24.32 × 10^-2 N F' = 0.2432 N Rounding to three decimal places: F' = 0.243 N Got more? Send 'em 📸