Ampère’s law

Definition

Ampère’s law is a fundamental principle in electromagnetism that relates the integrated magnetic field around a closed loop to the electric current passing through the loop. Mathematically, it is expressed as $\oint_{C} \mathbf{B} \cdot d\mathbf{l} = \mu_{0} I_{enc}$, where $\mathbf{B}$ is the magnetic field, $d\mathbf{l}$ is an infinitesimal element of the loop, $\mu_{0}$ is the permeability of free space, and $I_{enc}$ is the total current enclosed by the loop.

5 Must Know Facts For Your Next Test

1. Ampère’s law can be used to calculate magnetic fields for highly symmetric configurations such as infinite straight wires, solenoids, and toroids.
2. The law is an integral form that relates magnetic field circulation around a closed path to the total enclosed current.
3. It assumes steady currents (time-independent), which means it does not account for changing electric fields.
4. The differential form of Ampère's law includes Maxwell's correction: $\nabla \times \mathbf{B} = \mu_{0}(\mathbf{J} + \epsilon_{0}\frac {\partial \mathbf{E}}{\partial t})$, where $\epsilon_{0}$ is the permittivity of free space.
5. Ampère’s law forms one of Maxwell’s equations, which are fundamental to classical electromagnetism.

Review Questions

• What does Ampère’s law mathematically relate?
• In what type of scenarios can Ampère’s law be easily applied?
• How does Ampère’s law change when considering time-varying electric fields?

Related terms

Magnetic Field ($\mathbf{B}$): A vector field that represents the influence exerted by magnetic forces on moving charges or magnetic materials.

Permeability of Free Space ($\mu_{0}$): A constant value that describes how much resistance is encountered when forming a magnetic field in a classical vacuum; its value is approximately $4\pi \times 10^{-7} \, T \, m/A$.

$I_{enc}$ (Enclosed Current): The total electric current passing through a surface bounded by a closed path in Ampère's law.