You need to insert a metal slab between the two plates of a parallel-plate capacitor. The plates are a distance \(d\) apart, and a battery maintains a constant potential difference \(V_{\text {batt }}\) between them. In order to avoid dielectric breakdown, the electric field in any region cannot exceed \(4 V_{\text {bat }} / d\).

(a) What is the maximum thickness of the metal slab that can be used without causing dielectric breakdown?

(b) If this maximum thickness is used, does the insertion of the metal slab affect the amount of charge stored on the capacitor?