Magnetic Flux (DP IB Physics)

Emf, Magnetic Flux & Magnetic Flux Linkage

• Magnetic flux is a quantity which signifies how much of a magnetic field passes perpendicularly through an area

• It is defined as:

  The product of the magnetic flux density and the cross-sectional area perpendicular to the direction of the magnetic flux density

• Magnetic flux when the field and motion are at 90° can be calculated using the simple equation:

• Where:

  • Φ = magnetic flux (Wb)

  • B = magnetic flux density (T)

  • A = cross-sectional area (m²)

• it is defined by the symbol Φ (greek letter ‘phi’) and measured in units of Webers (Wb)

How does magnetic flux change with angle?

• Since the flux is the total magnetic field that passes through a given area

  • It is a maximum when the magnetic field lines are perpendicular to the plane of the area

  • It is zero when the magnetic field lines are parallel to the plane of the area

• For a coil, the amount of magnetic flux varies as the coil rotates within the field

The magnetic flux is maximum when the magnetic field lines and the area they are travelling through are perpendicular

• In other words, magnetic flux is the number of magnetic field lines through a given area

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

• The equation then becomes:

Φ = BA cos(θ)

• Where:

  • Φ = magnetic flux (Wb)

  • B = magnetic flux density (T)

  • A = cross-sectional area (m²)

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

The magnetic flux increases as the angle between the field lines and plane decreases

• This means the magnetic flux is:

  • Maximum = BA when cos(θ) =1 therefore θ = 0^o. The magnetic field lines are perpendicular to the plane of the area

  • Minimum = 0 when cos(θ) = 0 therefore θ = 90^o. The magnetic field lines are parallel to the plane of the area

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:

Magnetic flux linkage =

• 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)

• 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 θ

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

• Magnetic flux linkage also changes with the rotation of the coil

  • It is at a maximum when the field lines are perpendicular to the plane of the area they are passing through

  • This is the same pattern as the magnetic flux 

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

ΦN = BAN cos(θ)

• Where:

  • N = number of turns of the coil