Displacement current goes through the gap between the plates of a capacitor when the charge of the capacitor

Options

A. is changing with time
B. decreases
C. does not change
D. decreases to zero

Explanation

To solve the question regarding when the displacement current goes through the gap between the plates of a capacitor, we can follow these steps:

### Step-by-Step Solution:

**Step 1: Understand the Concept of Displacement Current**
- Displacement current is a term introduced by James Clerk Maxwell to account for the changing electric field in situations where the electric field is not constant, such as in capacitors during charging or discharging.

**Step 2: Recall the Formula for Displacement Current**
- The displacement current \( I_d \) is given by the equation:
\[ I_d = \epsilon_0 \frac{d\Phi_E}{dt} \]
where \( \Phi_E \) is the electric flux and \( \epsilon_0 \) is the permittivity of free space.

**Step 3: Analyze the Electric Flux in a Capacitor**
- The electric flux \( \Phi_E \) between the plates of a capacitor is related to the charge \( Q \) on the plates. It can be expressed as:
\[ \Phi_E = \frac{Q}{A} \]
where \( A \) is the area of the plates.

**Step 4: Determine When the Displacement Current Exists**
- The displacement current will exist when the electric flux \( \Phi_E \) is changing. This change occurs when the charge \( Q \) on the capacitor is changing with time.

**Step 5: Identify Conditions for Changing Charge**
- The charge on the capacitor can either be increasing or decreasing. Therefore, the displacement current will be present when:
- The charge is increasing (charging the capacitor).
- The charge is decreasing (discharging the capacitor).

**Step 6: Conclusion**
- The displacement current goes through the gap between the plates of a capacitor when the charge of the capacitor is changing with time. This includes both increasing and decreasing charge scenarios.

### Final Answer:
The displacement current goes through the gap between the plates of a capacitor when the charge of the capacitor is changing with time.

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