Potential Difference from Given Efield

[SMA777]

Homework Statement

The electric field in a region is given by E=2x^2 i +3y j where the units are in V/m. What is the potential difference from the origin to (x, y) = (2, 2) m?

Homework Equations

E = -gradient of V

The Attempt at a Solution

- derivative of the x-component: 2/3 x^2 from 0 to 2 = -16/3 x
- derivative of y-component: 3/2y^2 from 0 to 2 = -6 y

And then I added them for −11&1/3 V
But this wrong. I'm shown the correct answer is -27 & 1/3 V

Any tips on how that could be? Thanks !

 

[ehild]

- derivative of the x-component: 2/3 x^2 from 0 to 2 = -16/3 x
- derivative of y-component: 3/2y^2 from 0 to 2 = -6 y

And then I added them for −11&1/3 V
But this wrong. I'm shown the correct answer is -27 & 1/3 V

Any tips on how that could be? Thanks !

It was integration, and the integral of x^2 is x^3/3, and there is no x or y after substituting x=2 and y=2.

The result is correct however.

ehild

 

[SMA777]

Oh ,that's right! I meant integrated, sorry.

Wait, but my answer guide says -27 & 1/3 V and the sum of my answers is −11&1/3 V ? So, how do I got from my integration to the -27 & 1/3 V? I tried just adding and, as you saw, got −11&1/3 V which was incorrect

 

[ehild]

The answer guides are wrong sometimes. Check if you copied the electric field correctly.

ehild