A parallel-plate capacitor with air between the plates and plate separation distance \(d\) is connected to a battery that maintains a potential difference \(V_{\text {batt }}\) between the plates. Sketch a graph of \(V\) as a function of \(x\) when \(x\) is defined as position between the plates, running from \(x=0\) at the surface of the positively charged plate to \(x=d\) at the surface of the other plate. Plot the points \(x=0, x=d / 4, x=d / 2, x=3 d / 4\), and \(x=d\). A slab that is made of a dielectric material and has a thickness of \(d / 2\) is inserted between the plates such that the midpoint of the slab thickness is at the position \(d / 2\) in the space between the plates. Sketch a graph of \(V(x)\) for the capacitor now. Comment on how your graph is affected by the magnitude of the bound charge induced on the surface of the dielectric slab.