Magnetic Flux passing through an area?

November 13, 2007 9:46 PM

Physicsfilter: Is the magnetic flux passing through an area Φ = BA or is it Φ = nBA*cos(θ)?

I just sat a Physics exam and my friend and I are not too sure which is the correct answer. He asked some teachers, but the answers (at the time of writing) aren't very satisfactory. Physicists and electrical engineers: what is it?!

posted by PuGZ to Education (10 answers total)

You are both right, sorta.

BA would be the answer when the field is normal to the plane.

nBACos[theta] would be the answer for a coil of N turns at some angle theta to the field.
posted by Loto at 9:57 PM on November 13, 2007

Oops, posted too soon.

The completely correct answer is Flux = Integral[ B * dA ]
posted by Loto at 9:59 PM on November 13, 2007

I think your formulation of the question here answers your question. What would n have to do with the magnetic flux through an area? The magnetic flux through an area depends on the area and the magnetic field. It doesn't matter what you coil around your area, unless you are interested in other things (like induced EMF).
posted by ssg at 10:01 PM on November 13, 2007

really, it is a vector equation: dΦ = B (dot) dA where B is the vector field and A is the vector normal to some infinitesimal area. if you integrate over an area, over which the flux is constant, you can rewrite it in the cosine form.
posted by sergeant sandwich at 10:12 PM on November 13, 2007 [1 favorite]

Could be two ways of expressing the same thing if you look at the first as a vector operation:
Φ = B.A = BAcosθ

The n is inconsistent though. As Loto points out, it's an indicator of N turns per unit length of a coil, but isn't absolutely required, depending on how you define the area A.
posted by cardboard at 10:13 PM on November 13, 2007

.. and if the flux and area normal point in the same direction, and there is only one turn, then the cosine equation reduces to the first form you have.
posted by sergeant sandwich at 10:14 PM on November 13, 2007

Φ = BA, for a non changing magnetic field and surface. For that equation, A is the area that is perpendicular (this may be where your cos(θ) is coming from) to the magnetic field.

Hyperphysics is a great resource for this kind of stuff. "n" should definitely have no play in that equation. My guess is that the problem involved calculating the induced voltage in a coil using Faraday's Law, and that's where the n is coming from.
posted by christonabike at 10:19 PM on November 13, 2007

BTW, physics forums is a great place to ask about physics or math in general.
posted by pravit at 10:31 PM on November 13, 2007

Loto has it right, it's simply BA. It sounds from the discussion you linked to that you are talking about the flux through a coil. A coil is effectively like a bunch of rings stacked together. The B field through a stack of rings is the same as a single ring. You could think of it as a tube shaped conductor and the current moving as a sheet around the tube. The result is that you have a constant B field throughout the length of the coil. The number of turns is irrelevant. So using Loto's equation:
Flux = Integral[ B dot dA ] where B is constant, and the cross section of the coil is perpendicular to axis, the result is just BA.
posted by JackFlash at 11:43 PM on November 13, 2007

I think the confusion here comes from careless use of the integral form of Faraday's law (found here). This is what you use when you want to find the EMF induced in a loop of wire by a changing magnetic field.

JackFlash and others are correct that the flux through a coil doesn't depend on the number of turns. However, the EMF between the ends does. The problem is that the integral requires a closed loop (due to Stokes' theorem), but a coil doesn't really have any closed loops. What you do is treat each turn of the coil as its own closed loop. Then, the EMF between the endpoints is the number of coils times the time rate of change of the flux (up to the sign). This is why the N appears in Faraday's law for coils in your textbooks.
posted by dsword at 5:03 AM on November 14, 2007