# Electric potential integral

1. Oct 6, 2011

### Strawer

1. The problem statement, all variables and given/known data

An electric field is given by E = 2xi-3y2j N/C. Find the change in potential from the position rA = i - 2j m to rB = 2i + i + 3k m.

2. Relevant equations

VB - VA = -$\int_A^B$ E$\cdot$ds

3. The attempt at a solution

ΔV= -$\int_1^2$2x dx - $\int$-3y^2 dy

The second integral is supposed to be from -2 to 1

And when I calculate this I get -10 V when the answer is +6 V

I also noticed that if I simply invert the limits on the integral I get +6 V, is it just a coincidence or have I calculated the integral wrong?

2. Oct 6, 2011

### ehild

You can have a sign error somewhere. Show your work.

ehild

3. Oct 6, 2011

### Strawer

Well i have noticed that i'm very prone to making rudimentary mistakes often but I don't believe that to be the case here.

When calculating the integral I do as follows:

- $\left[ x^2 \right]_{1}^{2}$ - $\left[ -y^3 \right]_{-2}^{1}$ =
-(4-1) - (-1+8)= -3 - 7 = -10 V

4. Oct 6, 2011

### ehild

You made the sign error at y^3. At the lower bound it is -(-(-(-8)))

-x^2-(-y^3)=-x^2+y^3.

-(4-1)+(1^3-(-2)^3)=-3+(1+8)=6

ehild

5. Oct 6, 2011

### Strawer

Oh I see now. My homework would be alot loss painful if I could avoid stuff like this but it doesn't matter how thorough I am, I often miss things anyways. I think I might have a mild form of dyscalculia or something..

But thank you for your assistance!

Last edited: Oct 6, 2011
6. Oct 6, 2011

### ehild

Get rid of the lot of minuses as soon as possible and use parentheses. No dyscalculia. I got the correct result at the fourth attempt.:rofl:

7. Oct 6, 2011

### Strawer

Hehe well it's good to know that i'm not the only one who struggles with stuff like that

8. Oct 6, 2011

### SammyS

Staff Emeritus
What is the z coordinate for rA ?

9. Oct 7, 2011

### Strawer

There isn't a z coordinate for rA but as I understand that doesn't matter anyways since the electric field has no component in the z direction.

10. Oct 7, 2011

### ehild

That is the z coordinate is 0.

ehild

11. Oct 7, 2011

### SammyS

Staff Emeritus
Yup , so rB - rA has a z component.

12. Oct 7, 2011

### ehild

It has, but E has not.

ehild