# Potential difference in uniform electric field

• Krushnaraj Pandya
In summary, the homework statement asks which is greater: the potential difference V(10√2,0) or V(0,0)? However, because V(b) - V(a) is positive, the answer is +1000.

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## Homework Statement

There is a uniform electric field=100 V/m inclined at 45 degrees with the x axis. My doubt boils to which is greater? V(0,0) or V(10√2,0) (since my answer has the wrong sign)

## Homework Equations

All electrostatics formulas

## The Attempt at a Solution

The work done to move a unit positive charge from origin to (10√2,0) is component of E on x axis*1 C*displacement. which works out to +1000 (since Force and displacement are in the same direction). Now W=-ΔU and ΔU/1 C =ΔV=-1000 but the answer is +1000. I would appreciate some help, thank you

Krushnaraj Pandya said:
which works out to +1000 (since Force and displacement are in the same direction).
That's the work done by the field as the charge moves from the origin to the given point.

Krushnaraj Pandya said:
Now W=-ΔU and ΔU/1 C =ΔV=-1000 but the answer is +1000.
The potential at the origin is indeed higher, but whether the "answer" is + or - depends on how it is worded. What's the exact wording of the question?

Doc Al said:
That's the work done by the field as the charge moves from the origin to the given point.

The potential at the origin is indeed higher, but whether the "answer" is + or - depends on how it is worded. What's the exact wording of the question?
correct. The exact wording is as follows "In a uniform electric field E=100 V/m, the potential difference V(a) - V(b), where AB=10√2 m, is?"
Then there's a small figure which I'll completely describe so as not to miss any information. There is a horizontal dotted line on which A and B are marked, the distance between them is marked as 10√2 m. equally spaced Electric field lines are drawn throughout and their angle with this horizontal line is marked as 45 degrees. (I transformed this information into the question I posted here)

Krushnaraj Pandya said:
their angle with this horizontal line is marked as 45 degrees
But are the arrows up to the right, up to the left, down to the left, or down to the right?

haruspex said:
But are the arrows up to the right, up to the left, down to the left, or down to the right?
up to the right (i.e. North-East).

Krushnaraj Pandya said:
up to the right (i.e. North-East).
Then I refer you back to DocAl's original response. The work done by the field on a 1C charge moving from A to B is +1000J. The work done by an external agent causing it to so move is therefore -1000J. The potential at A is 1000V higher than at B.

haruspex said:
Then I refer you back to DocAl's original response. The work done by the field on a 1C charge moving from A to B is +1000J. The work done by an external agent causing it to so move is therefore -1000J. The potential at A is 1000V higher than at B.
Ah, right- how silly of me to overlook that. Thank you very much for your help.

Krushnaraj Pandya said:
The exact wording is as follows "In a uniform electric field E=100 V/m, the potential difference V(a) - V(b), where AB=10√2 m, is?"
As I suspected, they asked for V(a) - V(b) but you calculated (correctly) ΔV = V(b) - V(a). That's why the "answer" was positive.

Doc Al said:
As I suspected, they asked for V(a) - V(b) but you calculated (correctly) ΔV = V(b) - V(a). That's why the "answer" was positive.
I am highly susceptible to the silliest mistakes possible. Even more so in Mathematics, there are times when I've begun typing a problem in PF after solving it incorrectly 5 times and while writing out "attempt at a solution" I realize I wrote 2+3 as 4 or something, I apologize for my lack of rigor, I am trying to be more accurate though.