Is My Calculation of Work Along a Defined Curve Correct?

[Morle]

Homework Statement

I would like to confirm whether my solution is correct.

Relevant Equations

vector line integral

I created a problem for myself, which I have documented in LaTeX. I hope it's acceptable that I included snapshots of my pages.

I would like to calculate the Work W along curve C1.

I have solved the problem as shown below. Is my solution correct (see Equation 1.11)?

The pictures I included are of low quality, so I've attached the main.pdf for your reference.

 

[Orodruin]

I am not opening unsolicited pdfs as a matter of principle.

Please note that the forum has LaTeX compatibility. You’ll have to change a couple of delimiters, but displaying equations written in LaTeX generally works quite well.

 

[nasu]

Your final result seems to have the wrong units.
But what's the point of doing this?

 

[Morle]

Hello Nasu, The goal is to improve my understanding by practicing vector line integral problems in physics, specifically those related to electrostatics. Why is the Unit of W not correct? q in [As], Q in [As], e0 in [As]/[Vm] so k in [As]*[Vm] and finally W in [As]*[Vm]/[m]=[VAs]=[Ws]=[Nm]=[J]. So the unit is correct, right?
Thanks and best regards.

 

[nasu]

What is the meaning of "m" in The denominator of your final result? It looks like "k" divided by some quantity in meters. Which does not have dimensions of work.