AcademyMagnetic Fields and Forces
Academy
Magnetic Flux
Level 1 - Physics topic page in Magnetic Fields and Forces.
Principle
Magnetic flux measures how much magnetic field passes normally through a surface.
Notation
\(\Phi_B\)
magnetic flux
\(\mathrm{Wb}\)
\(\vec B\)
magnetic field
\(\mathrm{T}\)
\(\vec A\)
area vector normal to a flat surface
\(\mathrm{m^{2}}\)
\(A\)
surface area
\(\mathrm{m^{2}}\)
\(\theta\)
angle between field and area vector
\(\mathrm{rad}\)
Method
The area vector points perpendicular to the surface. Flux is the dot product of field with area.
Uniform flat surface
\[\Phi_B=\vec B\cdot\vec A\]
Magnitude form
\[\Phi_B=BA\cos\theta\]
Curved surface
\[\Phi_B=\int\vec B\cdot d\vec A\]
Closed surface
\[\oint\vec B\cdot d\vec A=0\]
Gauss's law for magnetism says closed-surface magnetic flux is zero. Field lines do not begin or end on isolated magnetic charge.
Rules
Magnetic flux
\[\Phi_B=BA\cos\theta\]
Flux integral
\[\Phi_B=\int\vec B\cdot d\vec A\]
Weber
\[1\,\mathrm{Wb}=1\,\mathrm{T\,m^2}\]
No monopoles
\[\oint\vec B\cdot d\vec A=0\]
Examples
Question
A
\[0.30\,\mathrm{m^2}\]
loop is perpendicular to a \[0.40\,\mathrm{T}\]
field. Find the flux.Answer
\[\Phi_B=BA=(0.40)(0.30)=0.12\,\mathrm{Wb}\]
Checks
- Use the angle to the area vector, not the plane of the surface.
- Flux can be positive, negative, or zero depending on chosen normal.
- Net flux through a closed surface is zero for magnetic fields.