Final answer:
The capacitance of a capacitor increases when the distance between the plates is decreased due to the enhanced electric field that allows more charge to be stored for a given voltage. This relationship is defined by the formula C = Q/V.
Step-by-step explanation:
Why Capacitance is Inversely Proportional to the Distance Between Plates
The capacitance of a capacitor is defined as the ability to store charge per unit voltage. According to the properties of the electric field and the Coulomb force, capacitance should be inversely proportional to the distance between the capacitor's plates. When the distance (d) is reduced, the electric field, created by the separation of charges on the plates, becomes stronger because the charges are closer together and their attraction is increased. This stronger field allows for more charge (Q) to be stored for the same applied voltage (V), thus increasing the capacitance (C), as the relationship is given by the formula C = Q/V.
In a parallel-plate capacitor, which has plates with an area of A, separated by a distance d, if the distance is decreased while maintaining the same applied voltage, more electrons can be moved from the positive to the negative plate, resulting in more charge being stored and therefore a higher capacitance. The relationship between the charge, voltage, and capacitance in a capacitor demonstrates why a larger plate area results in higher capacitance, and conversely, why a smaller distance between plates also leads to higher capacitance.