Formula for Magnetic Flux (Uniform Magnetic Field)
The magnetic flux (Φ) through a plane surface in a uniform magnetic field (B) is given by Φ = B⋅A = BA cosθ, where A is the area and θ is the angle between B and the area vector.
What is Formula for Magnetic Flux (Uniform Magnetic Field)?
A measure of the total magnetic field passing through a given area. It is the dot product of the magnetic field vector and the area vector.
Key formula / rule: Magnetic Flux (Uniform Field)
Key points
- Define magnetic flux.
- Calculate magnetic flux through a planar surface in a uniform magnetic field.
- Identify the SI unit of magnetic flux.
- Understand the relationship between magnetic flux and the orientation of the surface relative to the magnetic field.
Common exam trap
Confusing the angle θ with the angle between the magnetic field and the surface itself (instead of the normal to the surface).
Definitions
- Term
Magnetic Flux
- Meaning
A measure of the total magnetic field passing through a given area. It is the dot product of the magnetic field vector and the area vector.
- Term
Area Vector
- Meaning
A vector perpendicular to a surface, with magnitude equal to the area of the surface.
- Term
Weber (Wb)
- Meaning
The SI unit of magnetic flux, equivalent to one Tesla-meter squared (Tm²).
Learning objectives
Define magnetic flux.
Calculate magnetic flux through a planar surface in a uniform magnetic field.
Identify the SI unit of magnetic flux.
Understand the relationship between magnetic flux and the orientation of the surface relative to the magnetic field.
Formulae
- Name
Magnetic Flux (Uniform Field)
- Note
Where B is magnetic field strength, A is area, and θ is the angle between B and the area vector (normal to the surface).
- Expression
Φ = B ⋅ A = BA cosθ
- Name
Magnetic Flux (General Surface)
- Note
Used for non-uniform fields or irregular surfaces.
- Expression
Φ = ∫ B ⋅ dA
Prerequisites
Vectors (dot product, angle between vectors)
Basic understanding of magnetic fields
Area of simple shapes
Common mistakes
Confusing the angle θ with the angle between the magnetic field and the surface itself (instead of the normal to the surface).
Incorrectly applying the formula for non-uniform fields or curved surfaces.
Forgetting to consider the direction of the area vector when calculating flux.
Unit conversion errors.
Keywords
Magnetic Flux
Uniform Magnetic Field
Area Vector
Weber
Electromagnetic Induction
Dot Product
Faraday's Law
Practice preview
A plane surface of area 0.007 m² has a magnetic flux of 4.9 x 10⁻⁴ Wb passing through it when placed in a uniform magnetic field of 0.1 T. What is the angle (in degrees) between the magnetic field and the area vector?…
hard
What is the formula for magnetic flux (Φ) through a plane surface of area A in a uniform magnetic field B, where θ is the angle between the magnetic field and the area vector?…
easy
What is the SI unit of magnetic flux?…
easy