The inner region A is a sphere of radius rₐ = 1, with charge density ρₐ = kr. The surrounding spherical shell B has outer radius rᵦ and charge density ρᵦ = 2k/r. Assume all quantities are in SI units. Which statement is correct?

Question

G1 Physics · Accepted Answer

For region A, rₐ = 1 and ρₐ = kr. Hence Qₐ = 4π∫₀¹ kr·r²dr = πk. For shell B, ρᵦ = 2k/r, so the charge from r = 1 to r = rᵦ is Qᵦ = 4π∫₁ʳᵦ (2k/r)r²dr = 4πk(rᵦ² - 1). Thus total charge is Q = πk(4rᵦ² - 3). For rᵦ = 3/2, Q = 6πk and the potential just outside B is V = Q/(4πε₀rᵦ) = (6πk)/(6πε₀) = k/ε₀. Therefore statement B is correct. For rᵦ = 2, Q = 13πk, so C is false; A and D are also inconsistent with the corresponding field values. Correct answer: B.