Two isolated solid conducting spheres of radii R and 2R are charged such that they have the same electrostatic potential. What is the ratio of the magnitudes of the electric fields at their respective surfaces ( E₁ : E₂ )?

Step-by-step solution

The electrostatic potential V at the surface of a conducting sphere of radius r and charge Q is given by V = 1 4 ₀ Q r . Since both spheres are at the same potential, V₁ = V₂ . The electric field E at the surface of a conducting sphere is given by E = 1 4 ₀ Q r^2 . This can be rewritten in terms of potential as E = V r . Since V is constant for both spheres, the electric field is inversely proportional to the radius ( E 1 r ). Therefore, the ratio of their electric fields is: E₁ E₂ = r₂ r₁ = 2R R = 2 1 The ratio is