The concentric spheres of radii R and r have positive charges q₁ and q₂ with equal surface charge densities. What is the electric potential at their common centre?

Step-by-step solution

Potential at the centre due to sphere with radius R , V₁= q₁ 4 ₀ R Potential at the centre due to sphere with radius r , V₂= q₂ 4 ₀ r Given, surface charge densities for both spheres = _ R = _ r i.e., aligned i.e., & q₁ 4 ₀ R² &= q₂ 4 ₀ r² & q₁ &= R² r² q₂ aligned Total potential at the centre due to both spheres aligned V &=V₁+V₂ &= q₁ 4 ₀ R + q₂ 4 ₀ r = 1 4 ₀ ( q₁ R + q₂ r ) &= 1 4 ₀ ( R² r² q₂ R )+ q₂ r = q₂ 4 ₀ ( R+r r² ) &= q₂ 4 r² ₀ (R+r)= ₀ (R+r) aligned