How does the spacing of capacitor plates affect its performance?

The spacing of capacitor plates plays a crucial role in determining the capacitance of the capacitor. Capacitance is defined as the ability of a capacitor to store charge, and it is mathematically expressed by the formula:

[ C = \frac{\varepsilon \cdot A}{d} ]

where ( C ) is the capacitance, ( \varepsilon ) is the permittivity of the dielectric material between the plates, ( A ) is the area of the plates, and ( d ) is the distance between the plates.

As the distance ( d ) between the capacitor plates increases, the capacitance ( C ) decreases. This occurs because a larger spacing makes it more difficult for the electric field to establish between the plates, thereby reducing the amount of charge the capacitor can store for a given voltage. Therefore, increasing the spacing between the plates adversely affects the performance of the capacitor by reducing its capacitance.

On the other hand, increasing the spacing does not inherently increase the stored charge, nor does it directly affect the dielectric strength or the magnetic field in a significant manner related to the capacitor's primary function. Thus, the relationship captured in choice B is key to understanding how capacitor performance is influenced by plate spacing