Electromagnetic Induction (Copy)

Magnetic Flux

• Magnetic flux (Φ) is defined as the product of the magnetic flux density (B) and the area (A) through which the field lines pass, perpendicular to the magnetic field.
• Formula:

  Φ = B × A

  Where:

  • Φ = magnetic flux (in webers, Wb)
  • B = magnetic flux density (T)
  • A = area perpendicular to the field (m²)
• If the magnetic field is at an angle θ to the normal of the surface, use:

  Φ = BA cosθ

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change A2 Level Physics Full Scale Course

Magnetic Flux Linkage

• Magnetic flux linkage is the total magnetic flux passing through all turns of a coil.
• Formula:

  Flux linkage = NΦ = NBA

  Where:

  • N = number of turns of the coil
  • Φ = magnetic flux through a single loop (Wb)
• Units of magnetic flux linkage: Weber-turns (Wb⋅turns)

Electromagnetic Induction: Key Experiments

1. Changing Magnetic Flux Induces E.M.F.

• Move a magnet in and out of a coil → an e.m.f. is induced.
• The faster the change in magnetic flux, the greater the induced e.m.f.

2. Direction of Induced E.M.F. Opposes the Change (Lenz’s Law)

• When north pole of a magnet is pushed into a coil:
  • Induced current creates a north pole on the near side → opposes the incoming magnet.
• When the magnet is pulled out:
  • Coil creates a south pole to oppose the motion outwards.

3. Factors Affecting Induced E.M.F.

• Number of turns in the coil (N)
• Magnetic flux density (B)
• Area (A) of the coil
• Speed of change in flux (rate of movement or change in B or A)

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change A2 Level Physics Full Scale Course

Faraday’s Law of Electromagnetic Induction

• The magnitude of the induced e.m.f. is directly proportional to the rate of change of magnetic flux linkage.
• Formula:

  E = −d(NΦ)/dt

  Where:

  • E = induced e.m.f. (V)
  • d(NΦ)/dt = rate of change of magnetic flux linkage (Wb⋅turn⁄s)

Lenz’s Law

• The direction of the induced e.m.f. is such that it opposes the change that caused it.
• The negative sign in Faraday’s law expresses Lenz’s law.
• It is consistent with the principle of conservation of energy:
  • Work must be done against the opposing magnetic effect to induce current.

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change A2 Level Physics Full Scale Course

Applications and Examples

Moving Magnet in Coil:

• Insert or withdraw a bar magnet through a solenoid.
• Observe deflection on a galvanometer.
• Larger deflection with faster motion or stronger magnet.

Rotating Coil in a Magnetic Field:

• Generates alternating current (a.c.) in the coil due to cyclical change in flux.
• Used in electric generators.

Transformer Action:

• Changing current in primary coil changes magnetic field.
• This changing field induces e.m.f. in secondary coil.

Key Equations Recap

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change A2 Level Physics Full Scale Course