Magnetic field strength (magnitude) produced by a long straight current-carrying wire

Definition

Magnetic field strength (magnitude) produced by a long straight current-carrying wire is the intensity of the magnetic field that surrounds the wire due to the flow of electric current through it. It can be calculated using Ampere's Law and is directly proportional to the current and inversely proportional to the distance from the wire.

5 Must Know Facts For Your Next Test

1. The magnetic field strength at a distance $r$ from a long straight current-carrying wire is given by $B = \frac{\mu_0 I}{2 \pi r}$, where $I$ is the current and $\mu_0$ is the permeability of free space.
2. $\mu_0$, known as the permeability of free space, has a value of $4 \pi \times 10^{-7} \, T \, m/A$.
3. The direction of the magnetic field produced follows the right-hand rule: if you point your thumb in the direction of the current, your fingers curl in the direction of the magnetic field.
4. The magnetic field strength decreases as you move further away from the wire ($B \propto \frac{1}{r}$).
5. Ampere's Law, which relates magnetic fields to electric currents, can be expressed as $\oint B \cdot dl = \mu_0 I_{enc}$ for a closed loop around a conductor.

Review Questions

• What formula would you use to calculate the magnetic field strength at a certain distance from a long straight current-carrying wire?
• How does increasing the distance from a long straight current-carrying wire affect its magnetic field strength?
• Describe how you would use Ampere's Law to find an expression for the magnetic field around a long straight wire.

Related terms

Ampere's Law: A fundamental law stating that for any closed loop path, the sum of lengths times their corresponding magnetic fields equals $\mu_0$ times the enclosed electric current.

Right-Hand Rule: A mnemonic used to determine directionality: pointing your thumb in direction of current flow lets your curled fingers show direction of surrounding magnetic field.

$\mu_0$ (Permeability of Free Space): $4 \pi \times 10^{-7} \, T \, m/A$, it represents how much resistance is encountered when forming a magnetic field in vacuum.