# Electric potential of electron

## Homework Statement

An electron is placed in an xy plane where the electric potential depends on x and y as shown in the figure (the potential does not depend on z). The scale of the vertical axes is set byVs = 500 V. In unit-vector notation, what is the electric force on the electron?

## The Attempt at a Solution

I tried evaluating the graph and seeing as it is a straight line for both the x and y components of the E field i was thinking i could get a partial derivative
∂V/∂x=-(-500v/0.4m)=1250N/C
∂V/∂y=-(100V/.4m)=-250N/C
I think this is where i went wrong.
anyhow, I went on to find the magnitude and direction of the E field
|E|=√(1250^2+250^2)=1274.75N/C
θ=tan^-1(-250/1250)=-11.31°
the next step given the force on an electron as F=qE
finding this for the separate components in vector notation give q=1.6*10^-19C
so F=(1.6*10^-19C)*[(1250N/Ci), (-250N/Cj)]
it is not the right answer so my understanding is failing at a point
thankyou

mfb
Mentor
Including the picture like this does not seem to work, but this link should work.
∂V/∂x=-(-500v/0.4m)=1250N/C
∂V/∂y=-(100V/.4m)=-250N/C
How did you get those 500 V and 100 V? The difference between 0 and 0.4 m looks larger in both pictures.

• w3dnesday
oh... derpy me thank you for pointing out my mistake... I know what i did now... i thought that was were i went wrong but i just could not see what it was

SammyS
Staff Emeritus
Homework Helper
Gold Member
Or maybe this way:

... so all can see it.

It might be helpful to explain what I did to make this image visible:

I used the Link provided by mfb .
I'll speculate that mfb looked into the Original Post someway in order to obtain the link.​

## Homework Statement

An electron is placed in an xy plane where the electric potential depends on x and y as shown in the figure (the potential does not depend on z). The scale of the vertical axes is set byVs = 500 V. In unit-vector notation, what is the electric force on the electron?