• 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

• 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)

• When the magnet 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

   

• 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 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:

ΦN =?BAN?cos(θ)

• Where:
  • N =?number of turns of the coil

   

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)