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The Biot-Savart Law provides a mathematical expression for the magnetic field intensity

**Expression:**

where:

\(\mathbf{B}\) = Magnetic flux density (magnetic field) at the point of interest (T, Tesla)\(\mu_0\) = Permeability of free space\((4 \pi \times 10^{-7} \, \text{H/m})\) \(I\) = Current flowing through the conductor (A, Amperes)\(\mathrm{d}\mathbf{l}\) = Infinitesimal element of the conductor carrying current\(I\) (vector)\(\mathbf{r}\) = Vector from the current element\(\mathrm{d}\mathbf{l}\) to the point where the magnetic field is being calculated- \(r\) = Magnitude of the vector
\(\mathbf{r}\) (distance from the current element to the point where the field is calculated)

**Explanation:**

- The Biot-Savart Law states that the magnetic field produced at a point in space is proportional to the current and inversely proportional to the square of the distance from the current element to the point.
- The cross product
\(\mathrm{d}\mathbf{l} \times \mathbf{r}\) indicates that the direction of the magnetic field is perpendicular to both the direction of the current and the vector pointing from the current element to the observation point.

**Applications:**

- The Biot-Savart Law is used to determine the magnetic field produced by complex current distributions, such as loops, solenoids, and other geometries.
- It is instrumental in calculating the magnetic fields in various engineering applications, such as designing magnetic circuits, electric motors, and transformers.