Match the physical quantities for a charged conducting sphere of radius R having a uniform surface charge density (List-I) with their corresponding expressions (List-II). List-I List-II (A) Electric field inside ( r (I) R^2 ₀ r (B) Electric potential inside ( r (II) 0 (C) Electric field outside ( r > R ) (III) R ₀ (D) Electric potential outside ( r > R ) (IV) R^2 ₀ r^2 Choose the correct answer from the options given

Step-by-step solution

For a conducting sphere of radius R with uniform surface charge density , the total charge is q = (4 R^2) . (A) Inside the conductor ( r (B) The electric potential inside the conductor is constant and equal to the potential at its surface: V = 1 4 ₀ q R = 1 4 ₀ (4 R^2) R = R ₀ . So, (B) matches (III). (C) The electric field outside the sphere ( r > R ) is E = 1 4 ₀ q r^2 = 1 4 ₀ (4 R^2) r^2 = R^2 ₀ r^2 . So, (C) matches (IV). (D) The electric potential outside the sphere ( r > R ) is V = 1 4 ₀ q r = 1 4 ₀ (4 R^2) r