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 region and apply Gauss's law. Since r = 0.4\ m > R = 0.3\ m, the Gaussian surface is a sphere of radius r enclosing the total charge Q. Gauss's law: E · dA = Q_encl_0 Step 2: For spherical symmetry, E is constant on the Gaussian surface and perpendicular to it. E · 4 r^2 = (Q)/(_0) Step 3: Solve for E. E = (Q)/(4 _0 r^2) Step 4: Substitute constants. Use k = (1)/(4 _0) = 9.0 × 10^9\ N · m^2 / C^2. E = k (Q)/(r^2) Step 5: Plug in values: Q = 5.0 × 10^-9\ C, r = 0.4\ m. E = (9.0 × 10^9) 5.0 × 10^-9(0.4)^2 Step 6: Simplify numerator and denominator. E = (9.0 × 10^9)(5.0 × 10^-9) ÷ 0.16 E = 45 ÷ 0.16 Step 7: Compute the value. E = 281.25\ N/C 281 N/C