The magnetic field (B) created by an infinite line of current (I) at a distance (r) from the line is given by: *B = (μ₀ I) / (2πr)**.
Explanation
This formula describes the magnitude of the magnetic field. Let's break it down:
- B: Represents the magnetic field strength, typically measured in Tesla (T).
- μ₀: Represents the permeability of free space, a constant value approximately equal to 4π × 10⁻⁷ T⋅m/A.
- I: Represents the current flowing through the infinite line, measured in Amperes (A).
- r: Represents the perpendicular distance from the line to the point where the magnetic field is being measured, measured in meters (m).
The magnetic field lines form circles around the wire. The direction of the magnetic field is determined by the right-hand rule: If you point your right thumb in the direction of the current, your fingers will curl in the direction of the magnetic field. The magnetic field is tangential to a circle centered on the wire, with the wire as its axis.
Characteristics of the Magnetic Field
- Magnitude: The strength of the magnetic field is inversely proportional to the distance from the line of current. This means the magnetic field is stronger closer to the line and weaker further away.
- Direction: The magnetic field lines form concentric circles around the line of current. The direction is determined by the right-hand rule.
- Dependence: The magnetic field strength is directly proportional to the current flowing through the line. A larger current produces a stronger magnetic field.
Formula in Vector Form (Cylindrical Coordinates)
In cylindrical coordinates, the magnetic field can be expressed as:
*B = (μ₀ I) / (2πr) φ̂**
where φ̂ is the unit vector in the azimuthal direction (tangential to the circle around the wire).
Idealization
It's crucial to understand that an infinite line charge is an idealization. In reality, all wires have finite length. This formula provides a good approximation for the magnetic field near the center of a long, straight wire, provided the distance r is much smaller than the length of the wire.
