# Direction of work

1. Aug 18, 2011

### nouveau_riche

how can we account for the direction in which the work is being done by a particle while it is interacting?
say as an example,electron -electron repulsion,we know that there is a repulsive force but in which direction is the electron working(in direction of motion of force/any other)?

2. Aug 18, 2011

### LostConjugate

I would expect

The direction along the vector between the two electrons.

The force is in all directions but the force acting on another electron is along this vector. The sign depends on if your taking the electron to work on the other electron or itself.

3. Aug 18, 2011

### magpie5

Hi, when work is done, there must be some kind of enregy transfer or transformation eg from kinetic to kintec or potential to kinetic etc.
For two electrons interracting, say colliding, then one electron will gain an amount of energy due to the interraction and the other will loose an equal amount.
Because work deals with enegy which is a scalar, then there is no direction associated with this. One electron does work on the other and vis versa. It just depends on the question.

4. Aug 19, 2011

### nouveau_riche

which direction are you talking about,there will be many in between?

but you missed the nature of interaction ,repulsion/attraction
with collision an energy is gained/lost but the collision can occur from various direction,say head on or at 90 degree
what i mean to say is even if it is a head on,can u say it will always be repulsion?

5. Aug 19, 2011

### Staff: Mentor

Work does not have a direction. It is a scalar, not a vector.

6. Aug 19, 2011

### nouveau_riche

okay,let us talk about force in the same context,i mean electron electron interaction?

7. Aug 19, 2011

### sophiecentaur

The force will be along a line joining the electrons. The work will correspond to the integral of that force times distance (∫fdx)along that line.

8. Aug 19, 2011

### Staff: Mentor

The force between two stationary electrons is given by Coulomb's law and is always repulsive. The force between two moving electons is given by the Lienard Wiechert potentials and will also always be approximately repulsive, but due to the finite speed of light it may not always be pointing exactly directly away from the current position of the other electron.

9. Aug 19, 2011

### sophiecentaur

Yes, that must be right but will not each electron still 'see' a force which is radial? You would need to do a slightly modified line integral, possibly, but each electron would be accelerated along the line that it 'sees' the other one.

10. Aug 19, 2011

### Staff: Mentor

How would you would define a "radial force" in the case of an arbitrarily moving charge?

11. Aug 19, 2011

### sophiecentaur

It would be the same direction that the electron would look in order to see the other. That wouldn't be difficult to calculate, given the inclination, using a bit of SR. (Would it?)

12. Aug 19, 2011

### A.T.

Electrons are bad example for seeing each other. Take two negatively charged space ships at high relative speed.

13. Aug 19, 2011

### Staff: Mentor

I would have to work out the math to be sure, but I don't think that the force necessarily comes from that direction. For example, I think that the force from a charge moving at constant velocity comes from its actual position, but due to abberation you would look at a different position to see it. I am not certain about this, however, so don't rely too strongly on it.

14. Aug 19, 2011

### A.T.

This is correct. For inertial movement the field itself in the rest frame of the charge is static and radial, so the force is towards/from the charge. But light is a disturbance of the field that travels c. So the moving charge sees aberration.

In the rest frame of the "watching" charge the directions are different too, because the light comes from an old position of the light emitting charge. The field is Lorentz contracted, but moves with the charge and the force still points directly to the moving charge.

15. Aug 20, 2011

### nouveau_riche

how can you say that the force will be along the line joining the electrons?,i guess the direction of motion of electron is not the answer
how can you say that the force will be along the line joining the electrons?,i guess the direction of motion of electron is not the answer

16. Aug 20, 2011

### Staff: Mentor

I didn't say that. I said the force would be given by the Lienard Wiechert potential.

17. Aug 22, 2011

### nouveau_riche

can u explain that a bit?,and work will be a vector if the force is non conservative

18. Aug 23, 2011

### sophiecentaur

I can't see how a scalar can suddenly become a vector.??

19. Aug 23, 2011

### Staff: Mentor

Here is a good place to start: http://tinyurl.com/3aovkjz

No.

20. Aug 23, 2011

### ZealScience

I don't quite understand your question. What do you meant by direction of work? You can consider displacement as its direction, or you can consider the direction of the force as its direction. I think there is no difference between two vectors of the dot product or dot product integrated.

21. Aug 23, 2011

### nouveau_riche

well direction of work mean the path that will be followed by the test particle under the influence of source particle

i can prove this -- if a force is non conservative a line integral between two points will be different for different paths,so i will have to specify the directions along which a test particle moves under the influence of source

i can prove this -- if a force is non conservative a line integral between two points will be different for different paths,so i will have to specify the directions along which a test particle moves under the influence of source

22. Aug 23, 2011

### Staff: Mentor

Just because work done is path dependent in some cases does not make it a vector.

23. Aug 23, 2011

### FireStorm000

Work is the integral of F dot dr. That's the definition, plain and simple. What the dot product means is that the answer is the scalar magnitude of the force vector F projected along the length vector r. Because of this definition, the work done becomes a vector with one dimension of direction, + or -. So we make the important distinction that Energy is a scalar while Work is a vector. I just finished my AP Physics class not 3 months ago, so this is pretty fresh in memory. Work can either add or subtract from KE, PE, etc. In the case of a repulsive force, negative work is done, decreasing the KE and increasing PE. I believe what you're thinking of is the direction in which KE(Kinetic Energy) or the like is changing. If the electron is "climbing" a potential spike, then work done subtracts from KE, and if the electron is "falling" into a well, then the opposite is true. The justification is the definition of work and the nature of the force.

Also related is momentum, which is a vector quantity, and may be more what you're looking for. Momentum is the product of the scalar mass and vector velocity, which yields a second vector representing momentum. Force acting over time changes momentum.

24. Aug 23, 2011

### FireStorm000

http://physics.info/vector-multiplication/" [Broken]

Curiously, they list the dot product as producing a scalar. I guess what I'm getting from that is that there is some confusion/disagreement as to what constitutes a vector or a scalar. When I refer to a vector, it is any number with an attached direction, regardless of how many components that direction has. A scalar is any number that is independent of direction; a magnitude alone, without and direction, even + or -. Thus as I was taught, Work == Vector, Energy == Scalar. That might not be true if you choose to define vector/scalar quantities differently. If someone could clarify that inconsistency, I'd be much obliged.

Last edited by a moderator: May 5, 2017
25. Aug 23, 2011

### Staff: Mentor

Yikes!

Note that another name for the 'dot' product is the scalar product of two vectors. Quoting from hyperphysics: "The scalar product of two vectors can be constructed by taking the component of one vector in the direction of the other and multiplying it times the magnitude of the other vector." (See: http://hyperphysics.phy-astr.gsu.edu/hbase/vsca.html" [Broken])

Last edited by a moderator: May 5, 2017