Infinite straight wire

Definition

An infinite straight wire is an idealized concept in physics used to simplify calculations of electric and magnetic fields. It is assumed to extend infinitely in both directions with a uniform linear charge density.

5 Must Know Facts For Your Next Test

1. The electric field due to an infinite straight wire with linear charge density $\lambda$ at a distance $r$ from the wire is given by $E = \frac{\lambda}{2 \pi \epsilon_0 r}$.
2. The direction of the electric field produced by an infinite straight wire is always radially outward (or inward, depending on the sign of the charge) from the wire.
3. Gauss's Law is often used to derive the expression for the electric field around an infinite straight wire.
4. The symmetry of an infinite straight wire allows for simplifications in calculating the electric field using cylindrical coordinates.
5. An infinite straight current-carrying wire generates a magnetic field that circles around the wire, described by Ampère's Law.

Review Questions

• What is the formula for the electric field caused by an infinite straight wire with linear charge density $\lambda$?
• How does Gauss's Law help in calculating the electric field around an infinite straight wire?
• In which direction does the electric field point relative to an infinite straight wire?

Related terms

Linear Charge Density: Charge per unit length, denoted as $\lambda$, typically measured in coulombs per meter (C/m).

Gauss's Law: $$\oint \mathbf{E} \cdot d\mathbf{A} = \frac{Q_{enc}}{\epsilon_0}$$, a law stating that the total electric flux through a closed surface is equal to $$1/\epsilon_0$$ times the charge enclosed within that surface.

Ampère's Law: $$\oint \mathbf{B} \cdot d\mathbf{l} = \mu_0 I_{enc}$$, a fundamental law relating magnetic fields to the currents that produce them.