Physics Help Forum Area vector

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 Aug 14th 2018, 06:01 AM #1 Senior Member   Join Date: Mar 2009 Location: Yadupatti Bazar,Sitamarhi Posts: 137 Area vector In case of motional emf , if direction of magnetic field is perpendicular to the page of the paper and going into it and and a conductor is moving perpendicular to it. Then what will be direction of area vector and how ? __________________ If science solves one problem, it creates ten other problems.
 Aug 14th 2018, 10:59 AM #2 Physics Team   Join Date: Apr 2009 Location: Boston's North Shore Posts: 1,576 There's no such thing as an area vector. Please be more specific about what you're trying to learn.
Aug 14th 2018, 11:50 AM   #3

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 Originally Posted by ohm In case of motional emf , if direction of magnetic field is perpendicular to the page of the paper and going into it and and a conductor is moving perpendicular to it. Then what will be direction of area vector and how ?
Are you talking about the "area vector" on the cylinder? By definition the area vector would be perpendicular to the surface, which would make it pointing radially outward from the cylinder.

As Pmb says there really isn't such a thing as an area vector, but we can make a general definition that it is perpendicular to a surface and pointing "inward." We can get away with the concept and it's occasionally useful but it really isn't a vector.

-Dan
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Aug 14th 2018, 12:15 PM   #4
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 Originally Posted by topsquark Are you talking about the "area vector" on the cylinder? By definition the area vector would be perpendicular to the surface, which would make it pointing radially outward from the cylinder. As Pmb says there really isn't such a thing as an area vector, but we can make a general definition that it is perpendicular to a surface and pointing "inward." We can get away with the concept and it's occasionally useful but it really isn't a vector. -Dan
If we do that then such a vector is not unique. The vector you're referring to already has a name - surface normal.

 Aug 14th 2018, 09:43 PM #5 Senior Member   Join Date: Mar 2009 Location: Yadupatti Bazar,Sitamarhi Posts: 137 In a textbook , in case of motional emf this is given Case 1 plane is taken as plane of paper and direction of magnetic field is perpendicular to the plane of paper and inward. A conducting rod is moving perpendicular to the field but it's direction is not perpendicular to its length. Then the flux linked with area generated by the motion of rod in time t is Flux=BA cos0 I.e angle between field and area vector is taken as zero degree. Case 2. Again in the same plane a conducting rod is rotating in anticlockwise direction. The flux linked with area generated by Flux= BAcos180 I.e. angle between area vector and field is taken as 180 degree. Why angles are different? __________________ If science solves one problem, it creates ten other problems.
Aug 15th 2018, 02:09 AM   #6
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 Originally Posted by ohm In a textbook , in case of motional emf this is given Case 1 plane is taken as plane of paper and direction of magnetic field is perpendicular to the plane of paper and inward. A conducting rod is moving perpendicular to the field but it's direction is not perpendicular to its length. Then the flux linked with area generated by the motion of rod in time t is Flux=BA cos0 I.e angle between field and area vector is taken as zero degree. Case 2. Again in the same plane a conducting rod is rotating in anticlockwise direction. The flux linked with area generated by Flux= BAcos180 I.e. angle between area vector and field is taken as 180 degree. Why angles are different?
The area vector tells you about the magnitude of the area of a surface and the orientation of it.

The flux generated depends on the relative orientation of the field and the conducting area. It is the dot-product of the two quantities.

The dot-product makes use of the cosine function. This function is even, which means that it has a symmetric property such that for problems involving the comparison of two orientations, the results work out naturally, so you don't have to worry about "getting it wrong" by making the area vector point one way or the other.

For example; consider a field perpendicular to the surface so the area vector is parallel to the magnetic field strength. If we consider the two orientations of the area vector, we have
$\displaystyle \cos 0^o = 1$
$\displaystyle \cos 180^o = -1$

So the magnitude is the same in both cases. If your area vector is pointing in the opposite direction, the flux will be expressed relative to the area vector's orientation, so you'll get a negative flux in one orientation and a positive one in the other, indicating that there's only one direction in which the flux is travelling in. It works out naturally.

Last edited by benit13; Aug 16th 2018 at 05:39 AM.

 Aug 16th 2018, 04:52 AM #7 Senior Member   Join Date: Aug 2010 Posts: 434 More common is the differential "surface area vector" field. It is perpendicular to the surface at every point and its "length" is the differential of surface area, dA (which may be written as "dxdy" or "$\displaystyle rdrd\theta$". etc.).
Aug 16th 2018, 07:11 PM   #8
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 Originally Posted by HallsofIvy More common is the differential "surface area vector" field. It is perpendicular to the surface at every point and its "length" is the differential of surface area, dA (which may be written as "dxdy" or "$\displaystyle rdrd\theta$". etc.).
Its difficult to find in the math literature but not the physics literature. E.g. finding the total flux through a surface is used quite often in electrostatics, magnetostatics and electrodynamics.

Last edited by Pmb; Aug 16th 2018 at 09:48 PM.

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