Field due to an electric dipole (Halliday & Resnick, Ch. 27 problem 23)

AI Thread Summary
The discussion revolves around difficulties in calculating the electric field components \(E_x\) and \(E_y\) due to an electric dipole, referencing Halliday & Resnick's materials. Contributors emphasize the importance of presenting clear work and proper LaTeX formatting for effective communication. Specific advice includes using the "Preview" button to check LaTeX code and ensuring that all terms are correctly wrapped in braces. Additionally, when addressing "Show that" questions, it is crucial to include the initial expressions along with the final results. Clear formatting and thorough explanations are essential for collaborative problem-solving in physics.
Ben2
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Homework Statement
"Show that the components of ##\mathbf{E}## are given, at distant points, by [expressions below], where x and y are [coordinates of a point in the first quadrant...]." Here the dipole has charge q at (0,a) and charge -q are (0,-a).
Relevant Equations
$$E_x=\frac{1}{4\pi\epsilon_0}\frac{3pxy}{\left(x^2+y^2\right)^{(5/2)}}$$
$$E_y=\frac{1}{4\pi\epsilon_0}\frac{p\left(2y^2-x^2\right) }
{\left(x^2+y^2\right)^{(5/2)}}$$
Using either H&R's Chapter 27 Example 3 or Problem 590 of the ##\mathbf{Physics Problem Solver}##, I've been unable to get the component ##E_x## or ##E_y##. There are now different angles at the charges. My thanks to berkeman for LaTeX advice, but any errors are of course my own. Thanks in advance to all contributors!
 
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I see no errors mainly because I see no work. Please edit your post to fix the LaTeX.
Hint: Click the "Preview" button, last one on the right to see what your LaTeX will look like before committing yourself to posting.
Screen Shot 2024-04-12 at 2.22.58 PM.png
 
@Ben2 : Please wrap your last '5/2' term with {}.
 
Also, in a "Show that" type of question, in addition to what you are asked to "show" you must include the starting expression.
 
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