# CIE A Level Physics复习笔记20.2.1 Magnetic Flux

### Magnetic Flux Definition

• Electromagnetic induction is when an e.m.f is induced in a closed circuit conductor due to it moving through a magnetic field
• This happens when a conductor cuts through magnetic field lines
• The amount of e.m.f induced is determined by the magnetic flux
• The amount of magnetic flux varies as the coil rotates within the field
• 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 area
• It is at a minimum when the magnetic field lines are parallel to the area
• The magnetic flux is defined as:

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

### Calculating Magnetic Flux

• Magnetic flux is defined by the symbol Φ (greek letter ‘phi’)
• It is measured in units of Webers (Wb)
• Magnetic flux can be calculated using the equation:

Φ = BA

• Where:
• Φ = magnetic flux (Wb)
• B = magnetic flux density (T)
• A = cross-sectional area (m2)
• When the magnet field lines are not completely perpendicular to the area A, then the component of magnetic flux density B perpendicular to the area is taken
• The equation then becomes:

Φ = BA cos(θ)

• Where:
• 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 decreases as the angle between the field lines and plane decrease

• This means the magnetic flux is:
• Maximum = BA when cos(θ) =1 therefore θ = 0o. The magnetic field lines are perpendicular to the plane of the area
• Minimum = 0 when cos(θ) = 0 therefore θ = 90o. The magnetic fields 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 θ

#### Worked Example

An aluminium window frame has a width of 40 cm and length of 73 cm as shown in the figure below The frame is hinged along the vertical edge AC.When the window is closed, the frame is normal to the Earth’s magnetic field with magnetic flux density 1.8 × 10-5 T

a) Calculate the magnetic flux through the window when it is closed

b) Sketch the graph of the magnetic flux against angle between the field lines and the normal when the window is opened and rotated by 180°

Part (a)

Step 1:            Write out the known quantities

Cross-sectional area, A = 40 cm × 73 cm = (40 × 10-2) × (73 × 10-2) = 0.292 m2

Magnetic flux density, B = 1.8 × 10-5 T

Step 2:             Write down the equation for magnetic flux

Φ = BA

Step 3:            Substitute in values

Φ = (1.8 × 10-5) × 0.292 = 5.256 × 10-6 = 5.3 × 10-6 Wb

Part (b)

The magnetic flux will be at a minimum when the window is opened by 90o and a  maximum when fully closed or opened to 180o #### Exam Tip

Consider carefully the value of θ, it is the angle between the field lines and the line normal (perpendicular) to the plane of the area the field lines are passing through. If it helps, drawing the normal on the area provided will help visualise the correct angle. 