Distinguish between Biot Savart's law and Ampere's circuital law.

Explanation

To distinguish between Biot-Savart's Law and Ampere's Circuital Law, we can break down their definitions, applications, and characteristics step by step.

### Step 1: Definition
- **Biot-Savart's Law**: This law states that the magnetic field \( \mathbf{B} \) produced at a point in space by a small segment of current-carrying wire is directly proportional to the current \( I \), the length of the wire segment \( d\mathbf{l} \), and the sine of the angle \( \theta \) between the wire segment and the line connecting the wire segment to the point, and inversely proportional to the square of the distance \( r \) from the wire segment to the point. Mathematically, it is expressed as:
\[ d\mathbf{B} = \frac{\mu_0}{4\pi} \frac{I d\mathbf{l} \times \hat{r}}{r^2} \]

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