What work was done by the electric force?

[mvpshaq32]

Homework Statement

A particle with a charge of + 4.20 nC is in a uniform electric field E directed to the left. It is released from rest and moves to the left; after it has moved 6.00 cm, its kinetic energy is found to be +1.50 * 10^-6 J

What work was done by the electric force?

Homework Equations

W= -U = qEd

The Attempt at a Solution

I know the magnitude of the answer is 1.5 * 10^-6, but I'm having trouble with the sign. Since the field would naturally move the particle to the left, shouldn't the work be done by the electric force be negative? The force is not moving the particle against the direction of motion so it wouldn't be positive.

 

[gneill]

The problem didn't actually define the coordinate system, and in particular it didn't specify which direction(s) were to be taken as positive or negative. Since KE is always taken to be positive, the best you can say is that the work done has given the particle a certain speed, and it's perfectly reasonable to say that the work done was equal in magnitude to the change in kinetic energy.

 

[mvpshaq32]

Thanks gneill
Also, now that I think about it, shouldn't the work have be done by the field and instead of the electric force?

But otherwise, what would it mean by negative or positive work?
In my book there's a problem:

Two point charges are located on x-axis, q1=-e at x=0 and q2=+e at x=a. Find the work that must be done by an external force to bring a third point charge q3=+e from infinity to x=2a.

And its explanation is that if q3 is brought in from infinity along the +x-axis, it is attracted by q1, but is repelled more strongly by q2; hence positive work must be done to push q3 to position x=2a.

So my understanding is that if external force is against the field, then work is positive.

 

[gneill]

Yes, in one case it's the work done by the field on the particle that you're interested in; The electric force is due to the field. In the second case, it's the work done by the external force that is being considered.

 

[mvpshaq32]

Then does that mean we're looking at the work done by the field/electric force, it's positive if the particle is moving in the same direction as the field and negative when the particle is moving against the field?

 

[gneill]

Then does that mean we're looking at the work done by the field/electric force, it's positive if the particle is moving in the same direction as the field and negative when the particle is moving against the field?

The work done by a force is the integral of F.ds, where F and ds are vector quantities. The direction of the force produced by a field depends upon the sign of the charge on the particle. Similarly, the direction force required to bring a charged particle from infinity to some location in a field (without acceleration) will depend upon the direction of the field and the sign of the charge.

So, for example, if you had a positive charge at the origin and you wanted to bring another positive charge in from infinity, then an external force would have to push the charge along the direction of motion, and the work done by the external force would be positive. If the charge being brought in were negative, then the external force would have to "restrain" the charge from accelerating, and the work would be negative.

 

[mvpshaq32]

The work done by a force is the integral of F.ds, where F and ds are vector quantities. The direction of the force produced by a field depends upon the sign of the charge on the particle. Similarly, the direction force required to bring a charged particle from infinity to some location in a field (without acceleration) will depend upon the direction of the field and the sign of the charge.

So, for example, if you had a positive charge at the origin and you wanted to bring another positive charge in from infinity, then an external force would have to push the charge along the direction of motion, and the work done by the external force would be positive. If the charge being brought in were negative, then the external force would have to "restrain" the charge from accelerating, and the work would be negative.

Ok, so the way I'm interpreting your example is like this; If you bring a + charge from infinity towards a + charge at the origin, the field and the electric force will repel the charge to the right, but the external force will be towards the left (or the origin). If you bring a - charge from infinity towards a + charge at the origin, the field will still be directed to the right, but the electric force will be towards the origin and so you need a external force directed to the right. In the first case, the work done by the electric force is negative since it opposes the direction of motion and the work done by the external force is positive since it is along the direction of motion. In the second case, the work done by the electric force is positive since it is along the direction of motion and the work done by the external force is negative since it opposes the direction of motion.

And also, I'm still unclear on whether the work done by the electric field and the work done by the electric force is one and the same or are they different?

 

[gneill]

And also, I'm still unclear on whether the work done by the electric field and the work done by the electric force is one and the same or are they different?

It's the charge that produces the field (or rather, it's probably more correct to say that the field is a property of the charge). The field does work via the force it engenders in other charges. So I don't think you can say that they are 'different', as there's no way to separate one from the other. Fields inflict forces upon the objects that they interact with.

 

[mvpshaq32]

So work done by the field and work done by the electric force can be used interchangeably?

 

[gneill]

Yes.

 

[mvpshaq32]

Thanks for all the help gneill!