The weber (Wb) is the unit of magnetic flux in the International System of Units (SI). It is named after the German physicist Wilhelm Eduard Weber, who made significant contributions to the field of electromagnetism.
Magnetic flux is a scalar quantity that represents the total magnetic field passing through a given area, taking into account both the strength of the magnetic field and the orientation of the field lines with respect to the surface. The weber is used to quantify the overall effect of a magnetic field on a surface or within a closed loop, such as a wire coil in the case of electromagnetic induction.
One weber is defined as the magnetic flux that, when linking a circuit of one turn, produces an electromotive force of one volt as it is uniformly reduced to zero within one second. In other words, 1 Wb = 1 V⋅s (volt-second).
Mathematically, magnetic flux (Φ) is defined as the surface integral of the magnetic flux density (B) over an area (A). The formula for magnetic flux is:
Φ = ∫∫ B • dA
Where:
- Φ is the magnetic flux (measured in weber, Wb)
- B is the magnetic field vector (measured in tesla, T)
- dA is the differential area vector (measured in square meters, m²)
- • denotes the dot product
Magnetic flux plays a crucial role in understanding electromagnetic induction, as described by Faraday’s law of electromagnetic induction, which states that the electromotive force (EMF) induced in a closed loop is proportional to the rate of change of magnetic flux through the loop.
Examples of Magnetic Fluxes
Here are three examples of magnetic fluxes with values in weber:
- A circular loop with a radius of 0.03 m is placed in a uniform magnetic field of 0.4 T, perpendicular to the field lines. The magnetic flux through the loop is:
Φ = B * A = 0.4 T * (π * (0.03 m)²) ≈ 3.39 × 10⁻³ Wb
- A rectangular loop with a length of 0.05 m and a width of 0.03 m is oriented parallel to a uniform magnetic field of 0.6 T. Since the magnetic field lines are parallel to the plane of the loop, the magnetic flux is:
Φ = 0 Wb (no magnetic field lines pass through the loop)
- An equilateral triangular loop with a side length of 0.04 m is placed in a uniform magnetic field of 0.8 T, perpendicular to the field lines. The area of the triangle is A = (side² * √3) / 4. The magnetic flux through the loop is:
Φ = B * A = 0.8 T * ( (0.04 m)² * √3 / 4) ≈ 2.21 × 10⁻³ Wb
