# Uniform Field

1. Aug 29, 2009

### vin300

Moderation Note: Split from the original thread, which can be found https://www.physicsforums.com/showthread.php?p=680746#post680746"

A uniform field does not have potential difference

Last edited by a moderator: Apr 24, 2017
2. Aug 29, 2009

### Staff: Mentor

Re: Gravity inside the Earth

Really?

3. Aug 29, 2009

### vin300

Re: Gravity inside the Earth

It doesn't. Since the force everywhere is the same

4. Aug 29, 2009

Staff Emeritus
Re: Gravity inside the Earth

And force is the rate of change of potential.

5. Aug 29, 2009

### vin300

Re: Gravity inside the Earth

Right

6. Aug 29, 2009

### vin300

Re: Gravity inside the Earth

No Since the work done in bringing a unit mass from infinity to any point would be infinite, there is no potential difference

7. Aug 29, 2009

### vin300

Re: Gravity inside the Earth

Intuition works

8. Aug 29, 2009

Staff Emeritus
Re: Gravity inside the Earth

If the force is constant (and non-zero) and the potential is the rate of change of force, the potential cannot be constant.

That's simply not true.

I wouldn't trust it. It's leading you astray.

9. Aug 29, 2009

### vin300

Re: Gravity inside the Earth

The rate of change of potential is force
But not here

[qoute]
That's simply not true.[/quote]Why not true?The definition of potntial is the work done to bring a unit mass from infinity to a point, and is infinite here since the force is constant all over.In the classical case, force at infinity is zero

10. Aug 29, 2009

### vin300

Re: Gravity inside the Earth

Ah, you're too busy. I can see three in a line

11. Aug 29, 2009

### Staff: Mentor

Re: Gravity inside the Earth

The potential difference between any two points will be the work done to move a unit mass between those two points. (In some cases it makes sense to define the potential at infinity equal to zero, but not if the field is everywhere uniform.) Clearly the potential varies along the line of the force.

12. Aug 30, 2009

### vin300

Re: Gravity inside the Earth

True, but here the potential at every point in the field is infinite, so there's no difference

Last edited: Aug 30, 2009
13. Aug 30, 2009

Staff Emeritus
Re: Gravity inside the Earth

This is just plain wrong. You can't define the potential at one point to be infinity, then calculate that at another point it's also infinity, so the difference between them is zero. Apart from not being the way to solve the problem, this is mathematically incorrect.

A constant field has a potential growing linearly with distance.

14. Aug 30, 2009

### vin300

Re: Gravity inside the Earth

It is mathematically incorrect, the answer is actually uncertain.
I made use of the fact that since everywhere in the field the force on a unit mass is the same, the potential everywhere is the same too, but this does not go well with the math
There is no imbalance in this field, and hence there should be no potential difference.
But this is not real, and hence the answer is not real

Last edited: Aug 30, 2009
15. Aug 30, 2009

### Staff: Mentor

Re: Gravity inside the Earth

That "fact" is just plain wrong. Since the force = -dU/dx, the potential cannot be the same everywhere.

16. Aug 30, 2009

### Hootenanny

Staff Emeritus
Re: Gravity inside the Earth

I haven't read this thread in it's entirety, but I would like to comment on your last post:
As you say, this does not "go with the math" and is therefore incorrect! If there force on a unit mass is the same everywhere, that doesn't mean that potential is the same! In one dimension, the force is defined thus,

$$F = -\frac{dV}{dx}$$

We assume that the force is constant,

$$\frac{dV}{dx} = \text{const}$$

The potential is then (denoting the constant c1),

$$V = c_1x + c_2$$

Hence, the potential is not the same everywhere!

EDIT: Doc Al beat me to it

17. Aug 30, 2009

### vin300

Re: Gravity inside the Earth

Vanadium said that a lot earlier. And I replied "the potential at a point is the work done to bring a unit mass from infinity to that point and thus the potential everywhere in this field
is infinite"
There is no real answer to this because the situation itself is not real

18. Aug 30, 2009

### Hootenanny

Staff Emeritus
Re: Gravity inside the Earth

vin300 do you or do you not agree that the definition of force is the negative gradient of the potential? Please answer this question directly.

19. Aug 30, 2009

### DrGreg

Re: Gravity inside the Earth

Exactly the problem. There is no such place as "at infinity", so trying to calculate the potential "at infinity" is where your logic goes wrong. You can't treat infinity like a real number and try to do maths with it. Think about what's really happening, without bringing infinity into it, and you should be able to make sense of it.

When we say "it takes an infinite amount of work to move to infinity" you can't take that literally. It's a shorthand for saying, "the further you go, the more work is required, without any upper limit".

Don't forget that you can always add a constant to a potential, you don't have to evaluate it "at infinity" to decide what it is elsewhere.

20. Aug 30, 2009

### vin300

Re: Gravity inside the Earth

If you have read all my posts,:
Yes, I agree the force is the negative gradient of potential, this is a fact
Here there is a fixed force with an uncertain difference of potential, which is what makes the thing unreal

21. Aug 30, 2009

### Hootenanny

Staff Emeritus
Re: Gravity inside the Earth

Good, I'm glad we can agree on something.
This is where your error lies. If there is a constant (non-zero) force, then there must be a potential field that is a function of position. Please, disregard all your 'intuition' and simply follow the mathematics.

Now, concerning the mathematics, do you disagree with anything that I wrote in https://www.physicsforums.com/showpost.php?p=2326940&postcount=46" post?

Last edited by a moderator: Apr 24, 2017
22. Aug 30, 2009

### Staff: Mentor

Re: Gravity inside the Earth

OK.
This contradicts the previous sentence. (You are hung up on defining potential as work done from infinity. That certainly doesn't apply here.)

23. Aug 30, 2009

### vin300

Re: Gravity inside the Earth

Ok Now here I prove that the math you use for this problem is wrong
The definition of potential at a point that I already wrote twice is true.From that, you derive the formula of potential you used hitherto this way:
Integrate -(GM/r^2)dr with a lower limit of infinity and upper limit of r
But here, the force is independent of distance
Integrate -kGMdr with a lower limit of infinity and upper limit of r(where k=constant)
P=infinite, for any value of r
If you use this infinite potential to determine the PD you get an unreal answer
That because the situation is unreal
The beauty of it

Last edited: Aug 30, 2009
24. Aug 30, 2009

### Hootenanny

Staff Emeritus
Re: Gravity inside the Earth

Why is [negative] infinity an unreal answer here? Surely one would expect it to be infinite?

Your second integrand is equivalent to a constant force acting on an object. Now, suppose that object is moved through an infinite distance whilst being acted upon by a constant force. Surely it make sense that this would take an infinite amount of energy?

Or do you disagree?

25. Aug 30, 2009

### vin300

Re: Gravity inside the Earth

Exactly, but what is unreal is potential difference between two points in this field
oo-oo
I know you participated in that thread