A parallel-plate capacitor consists of square plates of edge length that are separated by a distance d,

A parallel-plate capacitor consists of square plates of edge length ℓ that are separated by a distance d, where d << ℓ. A potential difference ∆V is maintained between the plates. A material of dielectric constant 4 fills half of the space between the plates. The dielectric slab is now withdrawn from the capacitor, as shown in Figure P27.75.
a) Find the capacitance when the left edge of the dielectric is at a distance x from the center of the capacitor.
(b) If the dielectric is removed at a constant speed v, what is the current in the circuit as the dielectric is being withdrawn?