Maxwell in his famous equations of electro-magnetism introduced the concept of

Options

A. AC curent
B. DC current
C. displacement current
D. impendance

Explanation

**Step-by-Step Solution:**

1. **Understanding the Context**: Maxwell's equations are fundamental to electromagnetism. They describe how electric and magnetic fields interact and propagate. One of the key concepts introduced by Maxwell is the idea of displacement current.

2. **Charging a Capacitor**: When a capacitor is connected to a battery, it begins to charge. The charge on the capacitor plates increases over time, which leads to a change in the electric field between the plates.

3. **Defining Current Types**: In this scenario, we have two types of current:
- **Conduction Current (I_C)**: This is the current that flows through the conducting wire connected to the capacitor.
- **Displacement Current (I_D)**: This is a concept introduced by Maxwell to account for the changing electric field in the region between the capacitor plates, which can also create a current effect.

4. **Mathematical Representation**: The displacement current is mathematically represented as:
\[ I_D = \epsilon_0 \frac{d\Phi_E}{dt} \]
where \( \epsilon_0 \) is the permittivity of free space and \( \frac{d\Phi_E}{dt} \) is the rate of change of electric flux.

5. **Maxwell's Extension of Ampere's Law**: To maintain continuity in the loop of current, Maxwell modified Ampere's law. He stated that the total current \( I \) in a closed loop is the sum of the conduction current and the displacement current:
\[ I = I_C + I_D \]
This modification ensures that the law holds true even in regions where there is a changing electric field.

6. **Conclusion**: Therefore, the concept introduced by Maxwell in his equations is the displacement current, which arises due to the changing electric flux in a region.

**Final Answer**: The concept introduced by Maxwell in his famous equations of electromagnetism is the displacement current.

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