# Magnetic Flux Linkage(OCR A Level Physics)

## Revision Note

Author

Katie M

Expertise

Physics

• 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)

#### Worked example

A solenoid of circular cross-sectional radius 0.40 m and 300 turns is placed 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
• 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)

#### Exam Tip

Just like for magnetic flux, the flux linkage through a coil may not be entirely perpendicular.

The magnetic flux linkage through a rectangular coil increases as the angle between the field lines and a normal line to the coil plane decreases

In this case, you can just substitute the equation for B into the equation for φN, such that the flux linkage is calculated by:

As before, you should remember that since cos (0°) = 1, the flux linkage is a maximum when the angle θ is zero. This means the flux and coil face are perpendicular (i.e. the normal line to the coil face and the flux lines are parallel).

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