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
Here's the solution for problem 1.7: 1.7) A conducting sphere of diameter 20 cm is charged to a potential of 80,000V with respect to earth potential. Calculate the charge on the sphere assuming it to be situated in air. Given values: Diameter, D = 20 cm = 0.20 m Radius, r = (D)/(2) = 0.20 m2 = 0.10 m Potential, V = 80,000 V Permittivity of free space, _0 = 8.85 × 10^-12 F/m Step 1: Calculate the capacitance of an isolated conducting sphere. The capacitance C of an isolated conducting sphere in air (or vacuum) is given by the formula: C = 4 _0 r Step 2: Substitute the values into the capacitance formula. C = 4 (8.85 × 10^-12 F/m) (0.10 m) C ≈ 1.112 × 10^-11 F Step 3: Calculate the charge on the sphere using the relationship Q = CV. Q = (1.112 × 10^-11 F) × (80,000 V) Q = 8.896 × 10^-7 C The charge on the sphere is 8.90 × 10^-7 C. 3 done, 2 left today. You're making progress.