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Magnetic Flux AP Physics C Montwood High School R. Casao

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Magnetic flux is the number of magnetic field lines passing through a plane area A. Consider an element of area dA on an surface. If the magnetic field at this element is B, then the magnetic flux through the area is BdA, where dA is a vector perpendicular to the surface.

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The total magnetic flux m through the surface is: Consider a plane of area A and a uniform magnetic field B, which makes an angle with the vector dA:

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–If the magnetic field B lies parallel to the plane of the surface, the angle between B and dA is 90°. –The magnetic flux is zero because no magnetic field lines pass through the plane of the surface.

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–If the magnetic field B lies perpendicular to the plane of the surface, the angle between B and dA is 0°. –The magnetic flux is maximum and the greatest number of magnetic field lines pass through the plane of the surface.

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Remember that the angle is the angle between the magnetic field vector B and the area vector dA. The unit for magnetic flux is the weber (Wb). 1 Wb = 1 T·m 2 Flux Through a Rectangular Loop A rectangular loop of width a and length b is located a distance c from a long wire carrying current I. The wire is parallel to the long side of the loop.

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From Ampere’s law, the magnetic field due to the wire at a distance r from the wire is: The magnetic field B varies over the loop and is directed into the page. B is parallel to dA, so the magnetic flux through an element of area dA is:

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The magnetic field is not uniform throughout the area of the rectangular loop; it decreases in magnitude from length c to length c + a. Divide the length a into small elements of length dr. The area dA = b·dr.

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The contribution of each element of area dA to the total magnetic flux is: The total magnetic flux through the rectangular loop is determined by integrating from c to c + a.

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Evaluating the integral:

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Gauss’ Law in Magnetism Magnetic field lines are continuous and form closed loops. Magnetic field lines due to currents do not begin or end at any point. The magnetic field lines of a bar magnet illustrate the point. –For any closed surface, the number of magnetic field lines entering the surface is equal to the number leaving the surface. –The net magnetic flux is 0 T·m 2.

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Gauss’s law in magnetism states that the net magnetic flux through any closed surface is always zero. Gauss’ law in magnetism is based on the experimental fact that isolated magnetic poles (or monopoles) have not been detected, and may not even exist.

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The known sources of magnetic fields are magnetic dipoles (current loops). All magnetic field effects in matter can be explained in terms of magnetic dipole moments (effective current loops) associated with electrons and nuclei. Magnetic flux for multiple loops:

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