How do I Calculate V(ab) from E if A(-8,3,2) and B(5,2,3)?

[NWNINA]

Homework Statement

Calculate V(ab) if E = (-5 y / x^3) ax + (5/x) ay + 4 az V/m.
A(-8,3,2) and B(5,2,3).

Homework Equations

Vab=-∫Edl

The Attempt at a Solution

So I tried

V=-[∫(-5y/x^3)dx {from 5 to -8}+ ∫(5x)dy {from 2 to 3} + ∫4dz {from 3 to 2}]

The problem is that the limits are wrong. What should I do?
Should it be the distance and not the literal point on the plane? like the first one, should it be 0 to 13, the second one 0 to 1, the third one 0 to 1?
and what do I do with the remaining variables after the integration. For ex, in the first one I would have a y and on the second one a x

 

[Simon Bridge]

$$\vec{E}=-\frac{5y}{x^3}\hat{\imath} + \frac{5}{x}\hat{\jmath} + 4\hat{k} = \vec{\nabla}V$$What happens when you try to solve the system of DEs to get V(x,y,z).

Anyway - your approach $V_{AB} =\int_A^B \vec{E}\cdot d\vec{l}$ ...
... http://en.wikipedia.org/wiki/Line_integral#Line_integral_of_a_vector_field

 

[ehild]

Check if the electric field is conservative. If it is not, the work between a and b depends on the path, and potential is not defined.

ehild

 

[NWNINA]

Check if the electric field is conservative. If it is not, the work between a and b depends on the path, and potential is not defined.

ehild

It doesn't say anything about this.

 

[ehild]

Potential exist if the curl of the electric field is zero. Have you heard about that?
If not, check if you copied the formulas for E correctly, or any path is given in the problem. If you were supposed to integral for the path you used, note that when determining the integral for a line segment, the initial and final values of all variables have to been substituted. See figure.

ehild

 

[NWNINA]

Check if the electric field is conservative. If it is not, the work between a and b depends on the path, and potential is not defined.

ehild

I ended up reading a lot from the book, and yes it is conservative.
The book is just theory no example. So I don't really know the correct approach for this.
I think I'm going to go with V=-[∫(-5y/x^3)dx {from 5 to -8}+ ∫(5x)dy {from 2 to 3} + ∫4dz {from 3 to 2}]

and at the end, where I'm left with variables, substitute them for the coordinates from A

 

[ehild]

I ended up reading a lot from the book, and yes it is conservative.

The z component of the curl is not zero, so it is not conservative.

The book is just theory no example. So I don't really know the correct approach for this.
I think I'm going to go with V=-[∫(-5y/x^3)dx {from 5 to -8}+ ∫(5x)dy {from 2 to 3} + ∫4dz {from 3 to 2}]

and at the end, where I am left with variables, substitute them for the coordinates from A

The integral for the first line segment goes from (5,2,3) to (-8,2,3) (red line in the figure). The second integral goes from (-8,2,3) to (-8,3,3) (the blue line) and so on. You have to substitute the values of all variables.

ehild