magnetic flux

Magnetic Flux Definition, Unit, and Numerical Example notes in simple language

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Magnetic flux measures the magnetic field passing through a given surface. For a uniform magnetic field and a flat surface:

ΦB = B A cos θ

B = magnetic field (tesla, T); A = area (m²); θ = angle between the magnetic field and the surface normal. SI unit: weber (Wb); 1 Wb = 1 T·m². Magnetic flux is a scalar and may be positive, negative, or zero.

For a non-uniform field: ΦB = ∫ B · dA. Dimensional formula: [M L² T⁻² I⁻¹].

Important Cases of magnetic flux

  • θ = 0°: ΦB = BA (maximum positive flux; field perpendicular to the surface).
  • θ = 90°: ΦB = 0 (field parallel to the surface).
  • θ = 60°: ΦB = BA/2.
  • θ = 180°: ΦB = −BA (normal opposite to the field).

Remember: θ is measured from the normal to the surface, NOT from the plane of the surface.

Important Definition and Numerical Example

magnetic flux

A. Basic Facts About Magnetic Flux

  • Magnetic flux measures the total magnetic field passing through a given surface.
  • Magnetic flux is represented by the Greek letter Φ (Phi).
  • The SI unit of magnetic flux is the weber (Wb).
  • Magnetic flux is a scalar quantity.
  • The formula for magnetic flux is Φ = BA cos θ for a uniform magnetic field and a plane surface.
  • The dimensional formula of magnetic flux is [ML²T⁻²I⁻¹].
  • One Weber is equal to one tesla-meter squared (1 Wb = 1 T · m²).
  • The CGS unit of magnetic flux is the Maxwell (Mx).
  • 1 Weber = 10⁸ Maxwell.
  • Magnetic flux can be positive, negative, or zero depending on the chosen surface normal.

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B. Important Facts About Magnetic Flux and Angles

  • Magnetic flux is maximum when the magnetic field is perpendicular to the surface.
  • Magnetic flux is zero when the magnetic field is parallel to the surface.
  • When θ = 0°, magnetic flux is Φ = BA.
  • When θ = 90°, magnetic flux is Φ = 0.
  • When θ = 60°, magnetic flux is Φ = BA/2.
  • When θ = 30°, magnetic flux is Φ = √3BA/2.
  • When θ = 45°, magnetic flux is Φ = BA/√2.
  • When θ = 180°, magnetic flux is Φ = −BA.
  • The angle θ is measured between the magnetic field and the surface normal.
  • Magnetic flux depends on magnetic field strength, surface area, and orientation.

C. Magnetic Flux and Electromagnetic Induction

  • Michael Faraday discovered electromagnetic induction in 1831.
  • Electromagnetic induction is the production of EMF due to a change in magnetic flux linkage.
  • Faraday’s first law states that a changing magnetic flux linkage induces an EMF in a circuit.
  • Faraday’s second law states that induced EMF is equal to the negative rate of change of magnetic flux linkage.
  • The mathematical expression of Faraday’s law is ε = −N(dΦ/dt) for a coil of N turns with equal flux through each turn.
  • The negative sign in Faraday’s law represents Lenz’s law.
  • Lenz’s law states that induced current opposes the change in magnetic flux responsible for its production.
  • The SI unit of induced EMF is the volt (V).
  • One Volt is equal to one Weber per second (1 V = 1 Wb/s).
  • A changing magnetic flux can induce EMF even without direct contact between a magnet and a coil.

D. Magnetic Flux and Magnetic Field

  • Magnetic flux density is represented by B.
  • The SI unit of magnetic flux density is the tesla (T).
  • 1 Tesla = 1 Weber/m².
  • The CGS unit of magnetic flux density is Gauss (G).
  • 1 Tesla = 10⁴ Gauss.
  • Magnetic field lines form continuous closed loops.
  • Magnetic field lines never intersect each other.
  • The magnetic field is stronger where magnetic field lines are closer together.
  • The net magnetic flux through any closed surface is always zero.
  • Gauss’s law for magnetism is expressed as ∮ B · dA = 0.

E. Magnetic Flux and Practical Applications

  • An electric generator works on the principle of electromagnetic induction.
  • A transformer works on the principle of mutual induction.
  • An electric generator converts mechanical energy into electrical energy.
  • A transformer changes AC voltage through electromagnetic induction.
  • Eddy currents are circulating currents induced in conducting materials by changing magnetic flux.
  • Eddy currents are used in electromagnetic braking systems.
  • Laminated transformer cores help reduce energy losses due to eddy currents.
  • Magnetic flux linkage for a coil of N identical turns is NΦ.
  • The SI unit of magnetic flux linkage is Weber-turn (Wb-turn).
  • The induced EMF increases when the rate of change of magnetic flux linkage increases.
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