Magnetic Flux Linkage (AQA A Level Physics): Revision Note

Magnetic flux linkage

• More coils in a wire mean a larger e.m.f is induced

• 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:

$\mathrm{Magnetic}\mathrm{flux}\mathrm{linkage}=N\Phi =BAN$

• Where:

  • $\Phi$ = magnetic flux (Wb)

  • $N$ = number of turns of the coil

  • $B$ = magnetic flux density (T)

  • $A$ = cross-sectional area (m²)

• The flux linkage $N\Phi$ has the units of Weber turns (Wb turns)

Flux linkage in a rotating rectangular coil

• When the magnetic field lines are not completely perpendicular to the area A, then the perpendicular component of magnetic flux density B is taken

• The equation then becomes:

$\Phi =BA\cos \left(\theta \right)$

• Where:

  • $\Phi$ = magnetic flux (Wb)

  • $B$ = magnetic flux density (T)

  • $A$ = cross-sectional area (m²)

  • $\theta$ = angle between magnetic field lines and the line perpendicular to the plane of the area (often called the normal line) (degrees)

• This means the magnetic flux is:

  • Maximum = $BA$

    • when $\cos \left(\theta \right)=1$, therefore $\theta =0°$

    • The magnetic field lines are perpendicular to the plane of the area

  • Minimum = 0

    • when $\cos \left(\theta \right)=0$, therefore $\theta =90°$

    • The magnetic field lines are parallel to the plane of the area

• An e.m.f is induced in a circuit when the magnetic flux linkage changes with respect to time

• This means an e.m.f is induced when there is:

  • a changing magnetic flux density $B$

  • a changing cross-sectional area $A$

  • a change in angle $\theta$

• Magnetic field lines may not be completely perpendicular to the plane of the area that they pass through

• Therefore, the component of the flux density which is perpendicular is equal to:

$N\Phi =BAN\cos \left(\theta \right)$

• Where:

  • $N$ = number of turns of the coil