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

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SUMMARY

The discussion focuses on calculating the potential difference between points A(0,1) and B(1,0) using the electric field vector E = x(1 - sin(φ)) + y.cos(φ). The user successfully computed the potential difference along a circular arc but seeks guidance on calculating it along a straight line. The path integral of E dot dL, with a negative sign, is emphasized as the method for determining the potential difference.

PREREQUISITES
  • Understanding of electric field vectors and their components
  • Knowledge of line integrals in vector calculus
  • Familiarity with potential difference and its calculation methods
  • Basic trigonometry, particularly with angles and sine/cosine functions
NEXT STEPS
  • Study the concept of line integrals in vector fields
  • Learn about calculating potential differences in electrostatics
  • Explore the application of path integrals in physics
  • Review the properties of electric fields and their graphical representations
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Students and professionals in physics, particularly those studying electromagnetism, as well as engineers working with electric fields and potential differences.

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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