# Scalars and vectors.

## Homework Statement

Angular displacement, angular speed, , magnetic flux, electric potential, E.M.F., P.D., gravitational potential, stress,inductance. Which are the scalars and vectors?

## Homework Equations

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

## The Attempt at a Solution

I personally think, angular speed, electric potential, P.D, stress are scalars, but confused about others.

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berkeman
Mentor

## Homework Statement

Angular displacement, angular speed, , magnetic flux, electric potential, E.M.F., P.D., gravitational potential, stress,inductance. Which are the scalars and vectors?

## Homework Equations

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

## The Attempt at a Solution

I personally think, angular speed, electric potential, P.D, stress are scalars, but confused about others.

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.

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berkeman
Mentor
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.
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.?

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?

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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.

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Could someone help me here...fast?

berkeman
Mentor
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.
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.

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.
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.

berkeman
Mentor
BTW, a better term for flux would be flux density. Look at the definition of the Electric Flux Density vector D, for example.

vela
Staff Emeritus
Homework Helper
That would be changing the question though. Flux and flux density are different quantities, like mass and mass density.

berkeman
Mentor
That would be changing the question though. Flux and flux density are different quantities, like mass and mass density.
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).

vela
Staff Emeritus
Homework Helper
I think overall the wording is precise enough for unambiguous answers except, as you noted, for stress.

That would be changing the question though. Flux and flux density are different quantities, like mass and mass density.
Flux is calculated as (flux density*area). So whether it is supposed to have direction or not, is hard to judge.

vela
Staff Emeritus
Homework Helper
What's the general formula for flux?

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?

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.
Yes, therefore gravitational and electric field strengths are vectors.

I think overall the wording is precise enough for unambiguous answers except, as you noted, for stress.
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.

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vela
Staff Emeritus
Homework Helper
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?
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.?
Moreover, is not Pascal a scalar? I maybe wrong.
Units don't tell you anything. A force vector, for example, has units of Newtons, but so does its magnitude, which is a scalar.

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