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
To solve this problem, we will use the formula for electric potential due to a point charge and the formula for work done in moving a charge in an electric field. Given: Source charge Q = 2 microcoulomb = 2 × 10^-6 C Distance r_1 = 10 cm = 0.10 m Distance r_2 = 50 cm = 0.50 m Charge to be moved q = 0.05 microcoulomb = 0.05 × 10^-6 C = 5 × 10^-8 C Coulomb's constant k = 9 × 10^9 N m^2/C^2 The formula for absolute electric potential V at a distance r from a point charge Q is: V = (kQ)/(r) The formula for work W required to move a charge q from an initial potential V_A to a final potential V_B is: W = q(V_B - V_A) Step 1: Calculate the absolute potential at r_1 = 10 cm. V_1 = (kQ)/(r_1) V_1 = (9 × 10^9 N m^2/C^2)(2 × 10^-6 C)0.10 m V_1 = (18 × 10^3)/(0.10) V V_1 = 180 × 10^3 V V_1 = 1.8 × 10^5 V Step 2: Calculate the absolute potential at r_2 = 50 cm. V_2 = (kQ)/(r_2) V_2 = (9 × 10^9 N m^2/C^2)(2 × 10^-6 C)0.50 m V_2 = (18 × 10^3)/(0.50) V V_2 = 36 × 10^3 V V_2 = 3.6 × 10^4 V Step 3: Calculate the work required to carry the 0.05 microcoulomb charge from r=50 cm to r=10 cm. The initial potential is V_A = V_2 and the final potential is V_B = V_1. W = q(V_1 - V_2) W = (5 × 10^-8 C)(1.8 × 10^5 V - 3.6 × 10^4 V) W = (5 × 10^-8)(18 × 10^4 - 3.6 × 10^4