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In the below picture, what exactly is the streamline? Is it the three blue curves or is it the E vector drawn? Also, to calculate the equation of the streamline, we are using the ratio of the components of the E vector and setting that equal to the derivative at that point---is that correct?

enter image description here

Qmechanic
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David
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1 Answers1

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To answer your question, the "streamlines" are the blue curves, and that does appear to be an accurate interpretation of the caption.

That being said ... is this, by any chance, an introductory calculus textbook? I have never seen an integral curve of the electric field referred to as a streamline. They are usually called electric field lines, while the word streamline typically refers to an integral curve of the velocity field of some fluid. It's not strictly wrong, as the two objects are mathematically identical constructions, it just doesn't sound like something you'd find in a physics book.

Also, that is not typically how one solves for them because it runs into issues when $E_x=0$. The idea is more or less correct, but it's implemented differently to avoid this problem.

J. Murray
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  • this is from an electromagnetics textbook. Also, what exactly are we finding the equation for when we solve the differential equation at a specified point? Is it the equation of the blue curve? – David Sep 12 '18 at 04:49
  • Interesting. Which book, if I may ask? And yes - the blue curve is apparently given by some function $y(x)$, and that's what you're solving for. Though again ... that's not usually the best way to handle it in real life. – J. Murray Sep 12 '18 at 04:53
  • the book is "engineering electromagnetics by william hayt and john buck" eighth edition – David Sep 12 '18 at 04:54
  • i thought the equation was for the black vector (E vector)...how can the equation be for the entire blue curve if they specify a point? – David Sep 12 '18 at 04:55
  • The black vector is part of a vector field, which you can think of as a vector attached to each point in space. They only drew a single vector for clarity, but you already know $E_x$ and $E_y$ everywhere. – J. Murray Sep 12 '18 at 04:59