In your own words, explain the mechanism by which charge-storing capacity is increased by the insertion of a dielectric material within the plates of a capacitor.

A dielectric material is an insulating material that can be polarized by an electric field. When a dielectric material is inserted between the plates of a capacitor, it can affect the electric field, the charge distribution, and the voltage between the plates, ultimately increasing the charge-storing capacity of the capacitor.

When a dielectric material is placed in an electric field (such as between the plates of a capacitor), the electric field polarizes the molecules or atoms in the material. This causes the positive charges to be drawn towards the negative plate of the capacitor, and negative charges to be drawn towards the positive plate, creating a polarization within the dielectric. This polarization results in an induced electric field that opposes the original electric field created by the capacitor's plates.

The induced electric field produced by the dielectric material opposes the original electric field, reducing the overall electric field between the plates of the capacitor. This reduction in electric field causes a decrease in the voltage between the plates (V_new = V_old * (1 - E_induced/E_original)), leading to less energy required to store charges on the plates.

Since the voltage between the plates has been reduced, the charge-storing capacity (capacitance) of the capacitor is increased. The capacitance of a capacitor with a dielectric material can be described by the formula C_new = epsilon_r * C_old, where C_old is the original capacitance, epsilon_r is the relative permittivity of the dielectric material, and C_new is the new capacitance. As epsilon_r is always greater than 1 for a dielectric material, the capacitance will always increase when a dielectric material is inserted between the plates of a capacitor. In conclusion, inserting a dielectric material between the plates of a capacitor leads to a polarization, which reduces the electric field and voltage, resulting in an increase in the capacitor's charge-storing capacity.