Question

1. the capacitance of the capacitor proximity detector____when a nonconductive material is within range, and____when a conductive material is within range.

a. increases
b. decreases

Explanation:

When a non - conductive material (dielectric) is placed between the plates of a capacitor (in a capacitor proximity detector), the capacitance formula is \(C=\frac{\epsilon_0\epsilon_rA}{d}\), where \(\epsilon_r> 1\) for dielectrics (non - conductive materials). So, the capacitance increases. When a conductive material is within range, it acts like an additional plate and effectively reduces the distance \(d\) (by electrostatic induction, creating an image charge effect which is equivalent to a reduction in the separation between the effective plates of the capacitor - like a parallel plate capacitor with reduced \(d\)). Since \(C\propto\frac{1}{d}\) (from \(C = \frac{\epsilon_0A}{d}\) for a parallel plate capacitor with vacuum or air initially), a decrease in \(d\) causes an increase in \(C\).

Answer:

a. Increases, a. Increases