The electric potential at the center of two concentric half rings of radii R₁ and R₂ , having same linear charge density is ( ₀ = permittivity of free space)

Step-by-step solution

The electric potential V at the center of a uniformly charged circular arc of radius R and total charge Q is given by: V = 1 4 ₀ Q R For a half ring with linear charge density , the length of the arc is R . Therefore, the total charge on the half ring is: Q = ( R) Substituting this into the potential formula, the potential at the center due to one half ring is: V = 1 4 ₀ R R = 4 ₀ Notice that the potential at the center of a half ring depends only on the linear charge density and is independent of its radius R . Si