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Scalars and vectors.

  1. Sep 14, 2010 #1
    1. The problem statement, all variables and given/known data
    Angular displacement, angular speed, , magnetic flux, electric potential, E.M.F., P.D., gravitational potential, stress,inductance. Which are the scalars and vectors?



    2. Relevant equations
    Scalars are quantities, which have magnitude only, whereas vectors have both magnitude and directions.


    3. The attempt at a solution
    I personally think, angular speed, electric potential, P.D, stress are scalars, but confused about others.
     
  2. jcsd
  3. Sep 14, 2010 #2

    berkeman

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    (Thread moved from Advanced Physics to Intro Physics)

    Start with Angular Displacement -- does it have a direction?
     
  4. Sep 16, 2010 #3
    Well linear displacement has direction, so is not angular displacement also supposed to have direction. Linear speed does not have direction, so angular speed should also not have direction. Magnetic flux density is a vector, so magnetic flux is also supposed to be a vector. E.M.F. talks about electromotive force, and force is a vector, but E.M.F. defines energy, so I am confused. Direction of P.D. is considered in alternating currents, so it could be a vector. Gravitational and electric field strength is a vector, but what about gravitational and electric potential. Unit of stress is pascal, plus it is irrelevant of direction, therefore it is scalar. Inductance and capacitance are scalars as direction is not needed to describe them. Someone help quick, please.
     
    Last edited: Sep 16, 2010
  5. Sep 16, 2010 #4

    berkeman

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    Most of that is correct. Force may be a vector, but EMF is just a quantity in most cases. Look at the equations that define the EMF -- do they show EMF as a vector quantity?

    What is P.D.?
     
  6. Sep 17, 2010 #5
    No. It is defined more in terms of energy, so it is a scalar. P.D. is the potential difference that exists between any two points, at different potentials. Conventional current flows from higher positive potential to lower positive potential, is not that correct. Is it such that in a.c. the direction of E.M.F. only changes but every time the potential difference remains same, whatever the direction of E.M.F., it must be a scalar. Are gravitational and electric potentials vectors?

    Speeds and voltages are scalars. I'm confused by the wording about "gravitational and electric potentials" though. Potential energy is a scalar. But the gradient of each is a vector. What is the exact problem wording?
     
    Last edited by a moderator: Sep 17, 2010
  7. Sep 18, 2010 #6
    Does gradient mean gravitational field strength and electric field strength respectively? I found proof that this was a scalar, and was defined as work done in bringing unit mass or unit charge from infinity to a point in a uniform gravitational and electric field. Lets get this straight, angular displacement, magnetic flux, and other quantities like angular momentum, luminous flux, electric current are vectors. And those as gravitational potential, electric potential, stress, viscosity, illuminance, inductance and capacitance are scalars. Could you verify this? Thanks very much for your constant help berkeman.
     
    Last edited: Sep 18, 2010
  8. Sep 23, 2010 #7
    Could someone help me here...fast?
     
  9. Sep 24, 2010 #8

    berkeman

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    No, a taking the gradient of a potential field results in a vector. If you look up the definition of the gradient, you will find a vector definition in terms of unit vectors and partial derivatives in the directions of those unit vectors.

    http://en.wikipedia.org/wiki/Gradient

    I'm seeing a mix in what you are stating. Part of the problem may be a language issue, and an issue with definitions. With flux, for example, you will generally have a magnitude, and also a direction. The flux points in some direction, after all. But you can talk about the magnitude of the flux without talking about the direction in some cases -- like when using a light meter to measure luminous flux.

    I think you need to go back to the original question, and carefully list each separate thing in a rigerous way. Give an example equation for each quantity, and show how it is used. Once you do that, you should be able to say whether each has a direction associated with it.
     
  10. Sep 24, 2010 #9

    berkeman

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    BTW, a better term for flux would be flux density. Look at the definition of the Electric Flux Density vector D, for example.
     
  11. Sep 24, 2010 #10

    vela

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    That would be changing the question though. Flux and flux density are different quantities, like mass and mass density.
     
  12. Sep 24, 2010 #11

    berkeman

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    Agreed. Are the terms in the OP's first post precise enough that he can come up with unequivocal answers? A term like "stress" can mean multiple things, it seems to me (but I could be wrong).
     
  13. Sep 24, 2010 #12

    vela

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    I think overall the wording is precise enough for unambiguous answers except, as you noted, for stress.
     
  14. Sep 28, 2010 #13
    Flux is calculated as (flux density*area). So whether it is supposed to have direction or not, is hard to judge.
     
  15. Sep 28, 2010 #14

    vela

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    What's the general formula for flux?
     
  16. Sep 30, 2010 #15
    http://en.wikipedia.org/wiki/Flux" [Broken]

    Here flux is defined as both as scalar and vector, in terms of usage. Is not the general formula of flux, flux density(of a particular quantity)*area?

    Yes, therefore gravitational and electric field strengths are vectors.

    Stress is supposed to be scalar, because no matter what the direction of force the stress applied in the substance is the same, right?

    Moreover, is not Pascal a scalar? I maybe wrong.
     
    Last edited by a moderator: May 5, 2017
  17. Sep 30, 2010 #16

    vela

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    Well, you need to be a bit more precise. What type of multiplication are you referring to here? Is it scalar multiplication, the dot product, the cross product, etc.?
    Units don't tell you anything. A force vector, for example, has units of Newtons, but so does its magnitude, which is a scalar.
     
    Last edited by a moderator: May 5, 2017
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