1. The problem statement, all variables and given/known data Calculate the work done by a force, against an electric field, to bring a charged particle (2 coulomb) from the point (2,0,0) to (0,0,0). Also calculate the work from (0,0,0) to (0,2,0). Finally calculate the work done going directly from (2,0,0) to (0,2,0) and compare both results. The field is E= (2x, -4y) 2. Relevant equations dW= - q F dr 3. The attempt at a solution The only trouble I have is with the signs. I got 24 Joule in the last part, and -8 and 16 in the first two. I guess the -8 is wrong and it should be 8, so the sum is 24, as it should be in a conservative field. My attempt was: a) from (2,0,0) to (0,0,0) Here I think the differential of lenght is -dx, not dx, that is causing all the trouble. W= - (+2) * ∫ 2x * (-dx)= 4 * ∫x dx = 4 (x2/2) and this must be evaluated from 2, lower limit, to 0 upper limit. So I get: 4 ( 0 - 4/2) = -8 According to the book, the Work is: W=-2 ∫2x * dx , So he gets: + 8 Joules. CLearly he is using a differential of lenght positive, but x goes from 2 to 0, clearly from right to left, and clearly is just the opposite of the field that is 2x, which means is positive. So what I am doing wrong? In the work formula there is always a minus to show the applied force is opposite to the field, so once you have introduced that minus sign at the start of the formula, you don't need to specify in which direction the differential of lenght goes?