The electric-field magnitude at the centre of a uniformly charged hemispherical shell is E₀. Two portions are cut from the hemisphere as shown. If α = β = π/3 and the field due to the remaining portion is E = E₀/n, find n.

Question

G1 Physics · Accepted Answer

Using superposition, subtract the fields of the two removed symmetric portions from the field E₀ of the full hemisphere. For α = β = π/3, the surviving axial component is E₀/2. Therefore E = E₀/n = E₀/2, giving n = 2.