Finding V from E

1. Apr 23, 2013

NWNINA

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

2. Relevant equations

Vab=-∫Edl

3. 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

2. Apr 23, 2013

Simon Bridge

3. Apr 23, 2013

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

4. Apr 23, 2013

NWNINA

5. Apr 23, 2013

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

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6. Apr 24, 2013

NWNINA

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

Last edited by a moderator: Apr 24, 2013
7. Apr 24, 2013

ehild

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

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