- #1
Jake 7174
- 80
- 3
Homework Statement
Given the electric field E = (2x−y2)ax + (3z−2xy)ay + 3yaz, and the piecewise linear path joining the points A(−2,1,−1), P(2,1,−1), Q(2,3,−1) and B(2,3,1), find −∫E⋅dl from A to P − ∫E⋅dl from P to Q − ∫E⋅dl from Q to B along the straight line segments.
Homework Equations
−∫E⋅dl
(x - x1) / (x1 - x2 ) = (y - y1) / (y1 - y2 ) =(z - z1) / (z1 - z2 )
The Attempt at a Solution
I have solved this problem going direct from point a to b by using the above equation and found that the answer is 8 v. This is confirmed by the answer key. Here is my problem, when I set up the line equation to go from point A to P I get the following;
(x + 2) / (-2 - 2) = (y - 1) / (1 - 1) = (z + 1) / (-1 + 1)
or, (x + 2) / -4 = (y - 1) / 0 = (z + 1) / 0
I am ultimatley going to solve for y and z in terms of x to express my integral in terms of just x and I know how to get rid of the pesky dy and dz as well but I need the line equation to not blow up on me.
How do I resolve the division by 0? I know that the VAQ = 4 v from the solution but I am not sure what to do about the line equation.
I have an exam on Monday and I am certain a question like this will appear.
Last edited: