Electromagnetic Induction

• When a conducting wire moves through a magnetic field, a?potential difference?is created along the wire
  • If the wire is part of a closed circuit then an e.m.f is induced

• We can produce a?current?in a wire simply by moving a magnet near to it
  • Electrical energy is produced by the system since work is done on the wire by moving the magnet relative to the free electrons within it

• Therefore, electromagnetic induction is the term applied when an?e.m.f.?is induced in a closed circuit conductor due to it moving through a?magnetic field
  • Examples are a flat coil or a solenoid

• Electromagnetic induction happens when a conductor?cuts?through magnetic field lines
  • The amount of e.m.f induced is determined by the magnetic flux?and?the area on which the magnetic field acts

Magnetic Flux

• 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

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

• • Where:
    • Φ = magnetic flux (Wb)
    • B =?magnetic flux density(T)
    • A?= cross-sectional area (m2)

Changing Angle

• 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

• 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)

• 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

Part (a)

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 90°?and a maximum when fully closed or opened to 180°
• This is shown by the graph:

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 = ΦN = BAN

• • Φ =?magnetic flux?(Wb)
  • N?= number of turns of the coil
  • B?= magnetic flux density (T)
  • A?= cross-sectional area (m2)Where:

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

• 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
• 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