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
- Ampère’s law can be used to calculate magnetic fields for highly symmetric configurations such as infinite straight wires, solenoids, and toroids.
- The law is an integral form that relates magnetic field circulation around a closed path to the total enclosed current.
- It assumes steady currents (time-independent), which means it does not account for changing electric fields.
- 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.
- 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?
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Subjects (2)
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.
