# Potential difference between two points in an electric field

• NoahCygnus
In summary, the conversation is about calculating the potential difference between two points in a uniform electric field. One person argues that it is -20V while the other says it is -10√2V. The disagreement arises from using different values for the distance between the points, with one person using 1m and the other using √2m. The correct value is -20V, which can be found using the formula ΔV = -EΔr.

#### NoahCygnus

Homework Statement
In the problem, I have to calculate the potential difference between C and A as in the uniform electric field of magnitude 20 V/m given in the figure.
Relevant Equations
##\Delta V = -\vec{E}\cdot\Delta\vec{r}##
So I have been given a uniform electric field ##\vec{E}=20 V/m## in the direction as show in the image. I have been told to calculate the potential difference ##VC - VA##. According to the teacher (on YouTube) the potential difference ##VC - VA = -10\sqrt{2}V##. But I say it's ##-20 V## as electric field is conservative and I can find potential difference as work done in moving a unit charge from ##A## to ##D## then to ##C##. Potential difference between ##D##and ##A## should be a big zero as we are moving perpendicular to the field and potential difference between ##C## and ##D## is ##-20V## so the overall potential difference between ##C## and ##A## should be ##-20V## and not ##-10\sqrt{2}##.

They used ##\Delta V = -\vec{E}\cdot\Delta\vec{r}##, and put in the values ##\Delta V = -(20)(1)cos(45)=-10\sqrt{2}##

#### Attachments

• physics.jpg
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Their problem is that the length of the diagonal is not 1 m, it is ##\sqrt 2## m.

Edit: You should probably also link to the relevant video if it is on YouTube.