Calculating Potential Difference Between A(0,1) & B(1,0)

AI Thread Summary
To calculate the potential difference between points A(0,1) and B(1,0) in the given electric field E=x(1-sin(phi))+y.cos(phi), the potential V is determined through the path integral of E dot dL, with a negative sign. The user successfully solved the first part involving a circular arc but is seeking guidance on the second part, which involves a straight line connection between the two points. They have derived the line equation but are unsure how to proceed with the integration. Further assistance is requested to complete the calculation for the straight line path. The discussion highlights the challenges of applying path integrals in different geometries within electric fields.
brad sue
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Hi, I would like to have some suggestion about how to do this problem:

Given the electric field vector E=x(1-sin (phi))+ y.cos(phi)
x and y are unit vectors.
Calculate the potential difference between the points A(0,1) and B(1,0).
along :

1- Circular arc from(0,1) to (1,0)

2-straight line connecting (0,1) and (1,0)

thank you.
 
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V is the path integral of E dot dL, with a minus sign(convention).
 
I have succeeded to do the first question but how to do the second one. I found the line equation( I think it can help) but then I don't know how to continue.

B.
 
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