Points A (3 m, 3 m) and B (5 m, 7 m) are in a region where the electric field is uniform....?

Question

...and given by E = Ex i + Ey j, where Ex is 3 N/C and Ey is 4 N/C. What is the potential difference Va - Vb? Answer in units of V.

I wasn't really sure where to begin with this one. There's no charge given, and all I can come up with is that E should be the addition of Ey and Ex, or 7 N/C. I figured you have to first find out what Va is using this total E value, but I was sure which formula for electric potential to use to solve it. Any help would be appreciated.

Answer 1

Hi, I have this idea :

You know that, the potential difference is the minus integration of E.dr

E = Ex i + Ey j >>> The electrical field is a vector

The potential difference is a scalar value

But you have two values por E, one for Ex and aanother one for Ey, so dr = dx i + dy j

So :

The potential difference is : minus integration of ( Ex + Ey)*(dx + dy)

Is like a linear integration :

You will have :

minus integration of ( 3 i + 4j) (dx + dy ). Inner product

integration(3dx + 4dy)

x goes from : 3 to 5

y goes from : 3 to 7

minus integration ( 3*( 5 - 3 ))+(4(7-3)) = 6 + 16 = 22, and with the minus, it will be : -22

so the potential difference wil be = -22 V

I did it quickly, I hope that is the correct answer

Answer 2

Looks to me as though 7 is correct. The only issue is whether volts per meter is equivalent to newtons per coulomb, and at most there is a proportionality constant which is probably Eo, defined as 8.854E-12 farads per meter.

Answer 3

What?

Answer 4

Use E = - (V1 - V2)/(x1 - x2) ....enough hint?