The linear charge density on a dielectric ring of radius R varies with θ as λ=λ0cos(θ/2), where λ0 is constant. Find the potential at the center O of the ring [in volt].

The charge on the infinitesimal elements of arc that subtends an angle dθ at the center of the ring isdQ=λRdθ=λ0cos⁡θ2RdθPotential at the center of ring due to charge dQ isdV=14πε0dQR=λ0cos⁡θ2⋅Rdθ4πε0Ror V=∫dV=λ04πε0∫02π cos⁡θ2dθ=λ04πε0sin⁡θ21202π=0V