Question

A parallel plate capacitor is connected to a battery. As the plates are moved farther apart, what happens to each of the following? a) the potential difference across the plates b) the charge on the plates c) the electric field between the plates

Short answer

Short Answer: When the distance between the plates of a parallel plate capacitor is increased, the capacitance decreases, the potential difference across the plates increases, the charge on the plates remains constant, and the electric field between the plates remains constant.

Step-by-step solution

Understanding the formula for capacitance of a parallel plate capacitor

The capacitance of a parallel plate capacitor is given by the formula: C = (ε₀ * A) / d where C is the capacitance, ε₀ is the permittivity of free space (approximately 8.85 × 10⁻¹² F/m), A is the area of each plate, and d is the distance between the plates.

Relationship between charge, voltage and capacitance

The relationship between charge (Q), voltage (V), and capacitance (C) is given by the formula: Q = C * V

Analyzing potential difference across the plates

When the distance between the plates is increased, the capacitance decreases, as seen from the formula in Step 1. Since the capacitor is connected to a battery, the charge on the capacitor remains constant. Using the relationship in step 2 with constant charge, if the capacitance decreases, the voltage across the plates must increase. Therefore, the potential difference across the plates increases when the distance between them increases.

Analyzing the charge on the plates

As mentioned above, when the capacitor is connected to a battery, the charge on the capacitor remains constant. This is because a battery provides a constant voltage, and the capacitor is being charged to the same voltage. Therefore, the charge on the plates does not change when the distance between them is increased.

Analyzing the electric field between the plates

The electric field (E) between the plates of a capacitor is given by the formula: E = V / d Since the potential difference (V) increases when the distance (d) between the plates is increased (as described in Step 3), and since d is also increasing in the denominator, the overall effect on the electric field will depend on the relative change in V and d. However, in a parallel plate capacitor, the electric field is actually constant, as the field lines between the plates are uniform and perpendicular to the plates. So, the electric field between the plates will remain constant as the plates are moved apart.