Question Detail

According to Gauss's Law, for a spherically symmetric charge distribution or an enclosed charge within a spherical Gaussian surface, the electric field (E) on the surface is given by:E = Q / (4πε0r2)Where:Q = enclosed chargeε0 = permittivity of free space (8.854 × 10-12 F/m)r = radius of the sphere = 6 cm = 0.06 mE = electric field = 2.9 × 104 N/CWe can rearrange the formula to solve for Q:Q = E × (4πε0r2)We also know that k = 1/(4πε0) ≈ 9 × 109 N·m2/C2. So, 4πε0 = 1/k.Q = (E × r2) / kQ = (2.9 × 104 N/C × (0.06 m)2) / (9 × 109 N·m2/C2)Q = (2.9 × 104 × 0.0036) / (9 × 109)Q = 104.4 / (9 × 109)Q = 11.6 × 10-9 CTo convert to microcoulombs (µC), divide by 10-6:Q = 11.6 × 10-9 C = 0.0116 × 10-6 C = 0.0116 µCThis value is closest to 0.012 µC.