Biot-Savart law

Definition

The Biot-Savart Law describes the magnetic field generated by a steady current. It mathematically relates the magnetic field at a point to the current element and its position vector.

5 Must Know Facts For Your Next Test

1. It states that the magnetic field $d\mathbf{B}$ at a point due to an infinitesimal segment of current-carrying wire is directly proportional to the current $I$, the length of the segment $d\mathbf{l}$, and inversely proportional to the square of the distance $r$ from the segment to the point.
2. The Biot-Savart Law is given by: $$d\mathbf{B} = \frac{\mu_0}{4\pi} \frac{I d\mathbf{l} \times \hat{r}}{r^2}$$ where $\mu_0$ is the permeability of free space.
3. It applies to magnetostatics, which deals with steady currents producing constant magnetic fields.
4. The direction of $d\mathbf{B}$ is determined using the right-hand rule for cross products.
5. The Biot-Savart Law can be used to derive Ampère's Law in cases involving symmetrical current distributions.

Review Questions

• What are the variables in the Biot-Savart Law equation and what do they represent?
• How does distance affect the magnitude of the magnetic field according to Biot-Savart Law?
• In which situations would you use Biot-Savart Law over Ampère's Law?

Related terms

Ampère's Law:

Relates magnetic field in a loop to electric current passing through that loop, expressed as $$\oint \mathbf{B} \cdot d\mathbf{l} = \mu_0 I_{enc}$$.

Magnetic Permeability:

A measure of how much a material can support the formation of a magnetic field within itself, denoted by $\mu$. The permeability of free space is $\mu_0$.

Right-Hand Rule:

A mnemonic for understanding direction conventions in electromagnetism; for example, it helps determine direction of magnetic force or field vectors.