Ampere’s law

Definition

Ampere’s Law states that the line integral of the magnetic field $\mathbf{B}$ around any closed loop is equal to $\mu_0$ times the total current $I$ passing through the loop. Mathematically, it is expressed as $$\oint \mathbf{B} \cdot d\mathbf{l} = \mu_0 I_{enc}$$.

5 Must Know Facts For Your Next Test

1. Ampere’s Law is one of Maxwell’s equations, which are fundamental to electromagnetism.
2. It can be used to derive the magnetic field produced by a long straight current-carrying wire.
3. The law is valid for steady currents and provides a relationship between current and magnetic field.
4. $\mu_0$, known as the permeability of free space, has a value of $4\pi \times 10^{-7}$ T·m/A.
5. Ampere’s Law simplifies calculations in cases with high symmetry, such as solenoids and toroids.

Review Questions

• What does Ampere's Law state about the relationship between magnetic fields and electric currents?
• How does Ampere's Law help in calculating the magnetic field inside a solenoid?
• What is the significance of the constant $\mu_0$ in Ampere's Law?

Related terms

Magnetic Field ($\mathbf{B}$): A vector field surrounding magnets and electric currents, representing the force exerted on moving charges.

$\mu_0$ (Permeability of Free Space): $4\pi \times 10^{-7}$ T·m/A, a physical constant essential in calculating magnetic effects in vacuum.

Line Integral: A type of integral where a function is evaluated along a curve; used in Ampere’s Law to relate magnetic fields to current.