Displacement current exists between the plates of capacitor , when charge of the capacitor

Options

A. remains constant
B. increase
C. decreases
D. zero

Explanation

To determine when displacement current exists between the plates of a capacitor, we can analyze the situation step by step.

### Step-by-Step Solution:

1. **Understanding Displacement Current**: Displacement current is a term introduced by James Clerk Maxwell to account for the changing electric field in regions where there is no conduction current. It is given by the equation:
\[ I_d = \epsilon_0 \frac{dE}{dt} A \]
where \( I_d \) is the displacement current, \( \epsilon_0 \) is the permittivity of free space, \( \frac{dE}{dt} \) is the rate of change of the electric field, and \( A \) is the area of the plates.

2. **Capacitor Charging Process**: When a capacitor is connected to a battery, it starts to charge. The charge on the capacitor plates changes over time, which affects the electric field between the plates.

3. **Case of Zero Charge**: If there is no charge on the capacitor (i.e., it is uncharged), the electric field between the plates is zero. Since there is no electric field, there is no change in the electric field, and thus:
\[ I_d = 0 \]
Therefore, displacement current does not exist when the capacitor is uncharged.

4. **Case of Constant Charge**: If the charge on the capacitor is held constant (e.g., fixed at a certain value), the electric field between the plates remains constant. Since there is no change in the electric field:
\[ I_d = 0 \]
Hence, displacement current does not exist when the charge is constant.

5. **Case of Increasing or Decreasing Charge**: When the charge on the capacitor increases or decreases, the electric field between the plates changes. This change in electric field leads to a change in the displacement current:
\[ I_d \neq 0 \]
Therefore, displacement current exists when the charge on the capacitor is either increasing or decreasing.

### Conclusion:
Displacement current exists between the plates of a capacitor when the charge on the capacitor is changing (either increasing or decreasing).

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