Magnetic Flux Linkage
- The magnetic flux linkage is a quantity commonly used for solenoids which are made of N turns of wire
- Magnetic flux linkage is defined as:
The product of the magnetic flux and the number of turns
- It is calculated using the equation:
ΦN = BAN
- Where:
- Φ = magnetic flux (Wb)
- N = number of turns of the coil
- B = magnetic flux density (T)
- A = cross-sectional area (m2)
- The flux linkage ΦN has the units of Weber turns (Wb turns)
- As with magnetic flux, if the field lines are not completely perpendicular to the plane of the area they are passing through
- Therefore, the component of the flux density which is perpendicular is equal to:
ΦN = BAN cos(θ)
Worked example
A solenoid of circular cross-sectional radius of 0.40 m and 300 turns is positioned perpendicular to a magnetic field with a magnetic flux density of 5.1 mT.
Determine the magnetic flux linkage for this solenoid.
Step 1: Write out the known quantities
-
- Cross-sectional area, A = πr2 = π(0.4)2 = 0.503 m2
- Magnetic flux density, B = 5.1 mT = 5.1 × 10−3 T
- Number of turns of the coil, N = 300 turns
Step 2: Write down the equation for the magnetic flux linkage
ΦN = BAN
Step 3: Substitute in values and calculate
ΦN = (5.1 × 10−3) × 0.503 × 300 = 0.7691 = 0.77 Wb turns (2 s.f)
