Magnetic Flux
Magnetic flux is the total quantity of magnetic field lines passing perpendicularly through a given surface area, measuring how much of the magnetic field is captured by that surface. It is a scalar quantity defined as the dot product of the magnetic field vector and the area vector of the surface. Magnetic flux is fundamental to understanding electromagnetic induction, transformer operation, and the behaviour of inductors in circuits.
Key Formula
Φ_B = B × A × cos(θ)
LaTeX: \Phi_B = \vec{B} \cdot \vec{A} = BA\cos\theta
| Symbol | Meaning | Unit |
|---|---|---|
| Φ_B | Magnetic flux | Weber (Wb) |
| B | Magnetic field strength | Tesla (T) |
| A | Area of the surface | Square metres (m²) |
| θ | Angle between the magnetic field and the normal to the surface | Degrees or radians |
Worked Example
Problem
A rectangular coil of dimensions 0.2 m × 0.3 m is placed in a uniform magnetic field of 0.5 T. The normal to the coil makes an angle of 30° with the magnetic field. Calculate the magnetic flux through the coil.
Solution
Step 1: Identify the given values. B = 0.5 T, A = 0.2 × 0.3 = 0.06 m², θ = 30° Step 2: Apply the magnetic flux formula. Φ_B = BA cos θ Φ_B = 0.5 × 0.06 × cos 30° Step 3: Evaluate cos 30°. cos 30° = √3/2 ≈ 0.866 Step 4: Calculate. Φ_B = 0.5 × 0.06 × 0.866 = 0.02598 Wb
Answer
Φ_B ≈ 0.026 Wb (26 mWb)
Magnetic Flux for Different Orientations of a 0.06 m² Coil in a 0.5 T Field
| Angle θ (°) | cos θ | Flux Φ_B (Wb) | Description |
|---|---|---|---|
| 0 | 1.000 | 0.030 | Field perpendicular to surface — maximum flux |
| 30 | 0.866 | 0.026 | Partial alignment |
| 45 | 0.707 | 0.021 | Half-maximum flux |
| 60 | 0.500 | 0.015 | Reduced flux |
| 90 | 0.000 | 0.000 | Field parallel to surface — zero flux |
Interactive Tools
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Related Terms
Faraday's Law of Induction
Faraday's Law of Induction states that the electromotive force (EMF) induced in a closed loop is equal to the negative rate of change of magnetic flux through the loop. This fundamental law explains how changing magnetic fields produce electric currents, forming the basis of electric generators, transformers, and induction motors. It was discovered experimentally by Michael Faraday in 1831 and independently by Joseph Henry around the same time.
Lenz's Law
Lenz's Law states that the direction of an induced current is always such as to oppose the change in magnetic flux that caused it, thereby acting against the motion or change producing the induction. It is essentially a consequence of the conservation of energy and provides the negative sign in Faraday's Law of Induction. Named after Heinrich Lenz (1804–1865), the law explains why generators require mechanical work to produce electricity and underlies the principle of electromagnetic braking.
Electromagnetic Induction
Electromagnetic induction is the process by which a changing magnetic field within a closed conductor induces an electromotive force (EMF) and consequently an electric current in the conductor. Discovered by Michael Faraday in 1831, it is governed by Faraday's Law and Lenz's Law, and forms the operational basis of virtually all large-scale electrical power generation, transformers, and countless sensing devices. The phenomenon demonstrates the deep relationship between electricity and magnetism, first unified in Maxwell's equations.
From Latin "fluxus" meaning "flow" or "flowing", derived from "fluere" (to flow). The term was used by Michael Faraday in the 1830s to describe the flow of magnetic influence through space.