B = μ₀(i / (2πr))

Definition

This equation represents the magnetic field strength 'b' produced by a long, straight current-carrying wire at a distance 'r' from the wire. In this formula, μ₀ is the permeability of free space, and 'i' denotes the current flowing through the wire. Understanding this relationship is crucial for analyzing how electric currents generate magnetic fields and how these fields interact with other currents and magnetic materials.

5 Must Know Facts For Your Next Test

1. The constant μ₀ (permeability of free space) has a value of approximately 4π × 10^-7 T·m/A.
2. The formula indicates that the magnetic field strength 'b' is directly proportional to the current 'i' and inversely proportional to the distance 'r' from the wire.
3. As you move further away from the wire (increasing 'r'), the magnetic field strength decreases rapidly.
4. This equation is applicable primarily to long, straight wires; it may not hold true for wires that are coiled or have significant length compared to their diameter.
5. The direction of the magnetic field created by the current can be determined using the right-hand rule, which involves curling your fingers in the direction of the current while your thumb points in the direction of the magnetic field.

Review Questions

• How does the equation b = μ₀(i / (2πr)) demonstrate the relationship between current and magnetic field strength?
  • The equation b = μ₀(i / (2πr)) illustrates that as the current 'i' increases, the magnetic field strength 'b' also increases, demonstrating a direct relationship. Conversely, as the distance 'r' from the wire increases, 'b' decreases, indicating an inverse relationship. This formula helps to quantify how much influence a given amount of electric current has on its surrounding magnetic environment.
• Discuss how changes in distance from a wire affect the calculated magnetic field strength based on this equation.
  • According to b = μ₀(i / (2πr)), increasing the distance 'r' from a straight current-carrying wire results in a decrease in magnetic field strength 'b'. Specifically, because 'b' is inversely proportional to 'r', even small increases in distance can lead to significant reductions in magnetic field intensity. This principle is crucial for understanding applications like electromagnetic shielding and the behavior of circuits at various distances.
• Evaluate how this equation integrates with broader concepts such as Ampere's Law in understanding electromagnetism.
  • The equation b = μ₀(i / (2πr)) complements Ampere's Law, which states that magnetic fields can be generated by electric currents. By quantifying how much magnetic field is produced by a specific current at varying distances, this formula enhances our comprehension of Ampere's Law. Understanding both concepts together allows for deeper insights into circuit behavior, such as predicting how nearby currents will interact magnetically and formulating designs for efficient electromagnetic devices.

Related terms

Magnetic Field: A vector field that describes the magnetic influence of electric charges in relative motion and magnetized materials.

Permeability: A measure of how well a material can support the formation of a magnetic field within itself.

Ampere's Law:

A fundamental law relating the integrated magnetic field around a closed loop to the electric current passing through the loop.