6.6.2 Magnetic Flux Linkage

• The magnetic flux linkage is a quantity commonly used for solenoids which are made of N turns of wire
• The flux linkage is defined as:

The product of the magnetic flux and the number of turns of the coil

• It is calculated using the equation:

Flux linkage = 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)

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
  • 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 = 0.8 Wb turns (2 s.f)