Two parallel-plate capacitors with fixed plates are connected to two batteries as shown. The plate separation is the same in both. The rectangular plates have width b and lengths ℓ₁ and ℓ₂. The left and right halves of the common dielectric slab have dielectric constants K₁ and K₂. Neglect friction. Find the ratio of the left-battery emf to the right-battery emf for equilibrium of the slab.

Question

G1 Physics · Accepted Answer

Use Q = CV, U = ½CV² and C = εA/d; reduce the capacitor network by series/parallel combination and apply charge conservation where a node is isolated. The result matches A (V₁/V₂ = √[(k₂-1)/(k₁-1)]).