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How to do this question about calculating magnetic flux?

  • A coil with 50 turns and area 0.02 m^2 encloses a field that has a flux density of 100 X10^-6 T. The field is perpendicular to the plane of the coil. Q: What is the total flux enclosed? My answer is: Flux = B (flux density) X A = 100 X10^-6 X 0.02 = 2X10^-6 Tm^2 But then there are 50 coils so 50 X 2X10^-6 = 1X10^-4 Tm^2 (got this because the book says: hint - if a coil has N turns, the flux enclosed by the area of the coil is N*flux) Buuut then in the answer booklet it says the answer is 1 X10^-6 Tm^-2 Now I'm confused because I think this both the wrong answer and the wrong units. Or am I just being silly? Thanks

  • Answer:

    The flux, Φ, through the area, A, due to field B is given by: Φ = BA Φ = (100x10⁻⁶ T) x (0.02 m²) = 2x10⁻⁶ Tm² The more usual unit is the weber (Wb) but Tm² is technically correct. 1Wb = 1Tm². When you multiply this by the number of turns, the value is called the flux linkage, not flux; it is also measured in Wb (or Tm².) So in your question, flux linkage = NBA = 50 x 2x10⁻⁶ = 1x10⁻⁴ Wb (or Tm²) The book has several mistakes.

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The flux, Φ, through the area, A, due to field B is given by: Φ = BA Φ = (100x10⁻⁶ T) x (0.02 m²) = 2x10⁻⁶ Tm² The more usual unit is the weber (Wb) but Tm² is technically correct. 1Wb = 1Tm². When you multiply this by the number of turns, the value is called the flux linkage, not flux; it is also measured in Wb (or Tm².) So in your question, flux linkage = NBA = 50 x 2x10⁻⁶ = 1x10⁻⁴ Wb (or Tm²) The book has several mistakes.

Steve4Ph...

Technically, if you have N turns of a coil in a magnetic field, then they all experience the same amount of magnetic flux lines. It's like a set of rings being mounted on a stand; there's only one stand going through N number of rings. Likewise, drawing from this analogy, N coils of wire experience the same amount of magnetic flux as just one coil. So the answer should actually be (100x10^-6)T x 0.02, which is 2x10^-6 Tm^2. I'm not sure why the book says otherwise though. You're not being silly; but do inquire your teacher about this.

Jocelyne

Are you sure you calculated the are correctly? Remember, there are 10000 cm^2 in a m^2.

Joe

Technically, if you have N turns of a coil in a magnetic field, then they all experience the same amount of magnetic flux lines. It's like a set of rings being mounted on a stand; there's only one stand going through N number of rings. Likewise, drawing from this analogy, N coils of wire experience the same amount of magnetic flux as just one coil. So the answer should actually be (100x10^-6)T x 0.02, which is 2x10^-6 Tm^2. I'm not sure why the book says otherwise though. You're not being silly; but do inquire your teacher about this.

Jocelyne

Are you sure you calculated the are correctly? Remember, there are 10000 cm^2 in a m^2.

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