Go Back   Physics Help Forum > High School and Pre-University Physics Help > Electricity and Magnetism

Electricity and Magnetism Electricity and Magnetism Physics Help Forum

Like Tree1Likes
  • 1 Post By Pmb
Reply
 
LinkBack Thread Tools Display Modes
Old Aug 14th 2018, 07:01 AM   #1
ohm
Senior Member
 
Join Date: Mar 2009
Location: Yadupatti Bazar,Sitamarhi
Posts: 133
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.
ohm is offline   Reply With Quote
Old Aug 14th 2018, 11:59 AM   #2
Pmb
Physics Team
 
Join Date: Apr 2009
Location: Boston's North Shore
Posts: 1,569
There's no such thing as an area vector. Please be more specific about what you're trying to learn.
Pmb is offline   Reply With Quote
Old Aug 14th 2018, 12:50 PM   #3
Forum Admin
 
topsquark's Avatar
 
Join Date: Apr 2008
Location: On the dance floor, baby!
Posts: 2,466
Originally Posted by ohm View Post
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
__________________
Do not meddle in the affairs of dragons for you are crunchy and taste good with ketchup.

See the forum rules here.
topsquark is offline   Reply With Quote
Old Aug 14th 2018, 01:15 PM   #4
Pmb
Physics Team
 
Join Date: Apr 2009
Location: Boston's North Shore
Posts: 1,569
Originally Posted by topsquark View Post
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.
topsquark likes this.
Pmb is offline   Reply With Quote
Old Aug 14th 2018, 10:43 PM   #5
ohm
Senior Member
 
Join Date: Mar 2009
Location: Yadupatti Bazar,Sitamarhi
Posts: 133
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.
ohm is offline   Reply With Quote
Old Aug 15th 2018, 03:09 AM   #6
Senior Member
 
Join Date: Oct 2017
Location: Glasgow
Posts: 249
Originally Posted by ohm View Post
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 06:39 AM.
benit13 is offline   Reply With Quote
Old Aug 16th 2018, 05:52 AM   #7
Senior Member
 
Join Date: Aug 2010
Posts: 369
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.).
HallsofIvy is offline   Reply With Quote
Old Aug 16th 2018, 08:11 PM   #8
Pmb
Physics Team
 
Join Date: Apr 2009
Location: Boston's North Shore
Posts: 1,569
Originally Posted by HallsofIvy View Post
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 10:48 PM.
Pmb is offline   Reply With Quote
Reply

  Physics Help Forum > High School and Pre-University Physics Help > Electricity and Magnetism

Tags
area, vector



Thread Tools
Display Modes


Similar Physics Forum Discussions
Thread Thread Starter Forum Replies Last Post
Why is the product of a scalar and a vector, a vector? avito009 Physics 9 Apr 23rd 2018 04:28 PM
centroid of an area ling233 Kinematics and Dynamics 0 Nov 23rd 2015 03:51 AM
Unit vector is either a constant vector or not? rashidalishaikh Advanced Mechanics 1 Sep 7th 2013 07:17 AM
area of ellipse AStaunton Advanced Mechanics 0 Feb 24th 2011 05:49 PM
Fluids and area Apprentice123 Thermodynamics and Fluid Mechanics 1 Dec 2nd 2008 10:20 PM


Facebook Twitter Google+ RSS Feed