Write the mathmatical equation of Ampere-maxwell law.

Explanation

To write the mathematical equation of the Ampere-Maxwell Law, we will follow these steps:

### Step-by-Step Solution:

1. **Understanding the Ampere Circuit Law**:
The Ampere Circuit Law states that the line integral of the magnetic field \( \mathbf{B} \) around a closed loop is proportional to the total current passing through that loop. This includes both conduction current \( I_C \) and displacement current \( I_D \).

2. **Mathematical Representation**:
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