If conduction current is same as displacement current, then source is

Question

Accepted Answer

In the context of electromagnetic theory, the concept of displacement current is introduced by James Clerk Maxwell to address the inconsistency in Ampere's Law when applied to time-varying electric fields. Displacement current is not an actual current of moving charges, but rather a term added to Ampere's Law to account for the changing electric field in situations where there is no physical current.

1. **Explanation for Option 3 (Correct Answer):**  
   The displacement current is defined as the rate of change of electric displacement field (D) with respect to time. It is given by the equation:

$$
   I_d = \varepsilon_0 \frac{d\Phi_E}{dt}
   $$

where $ \varepsilon_0 $ is the permittivity of free space and $ \Phi_E $ is the electric flux. The conduction current, on the other hand, is the flow of electric charge through a conductor. In scenarios where the conduction current is equal to the displacement current, it implies that the electric field is changing with time in such a way that it can be associated with both alternating current (a.c.) and direct current (d.c.).

For a.c., the electric field inherently changes with time, leading to a displacement current. For d.c., while the field is generally constant, in transient states (such as when a circuit is switched on or off), the field can change, temporarily creating a displacement current. Therefore, both a.c. and d.c. can be sources where conduction current equals displacement current, justifying Option 3 as the correct answer.

2. **Explanation for why other options are incorrect:**

- **Option 1 (only a.c.):**  
     While it is true that a.c. involves a time-varying electric field, which naturally leads to a displacement current, it is not exclusive to a.c. As explained, d.c. circuits can also exhibit displacement currents during transient states. Therefore, limiting the source to only a.c. is incorrect.

- **Option 2 (only d.c.):**  
     Displacement current is typically associated with time-varying fields, which are more characteristic of a.c. However, as mentioned, d.c. can also have displacement currents during changes in the circuit state. Thus, stating that only d.c. can be the source is incorrect.

- **Option 4 (neither a.c. nor d.c.):**  
     This option is incorrect because both a.c. and d.c. can indeed be sources of displacement current under the right conditions. Displacement current is a fundamental concept that applies to both types of current in different scenarios, as explained above.

In conclusion, Option 3 is the correct answer because both a.c. and d.c. can be sources where conduction current equals displacement current, depending on the conditions of the electric field and circuit state.