184_notes:line_fields

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184_notes:line_fields [2019/01/04 00:55] – dmcpadden184_notes:line_fields [2021/02/13 18:58] (current) – [Building Electric Field for Lines of Charge] bartonmo
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 Sections 15.1-15.2 in Matter and Interactions (4th edition) Sections 15.1-15.2 in Matter and Interactions (4th edition)
  
-[[184_notes:dq|Next Page: dQ and the $\vec{r}$]]+/*[[184_notes:dq|Next Page: dQ and the $\vec{r}$]]
  
-[[184_notes:comp_super|Previous Page: Superposition and the Computer]]+[[184_notes:comp_super|Previous Page: Superposition and the Computer]]*/
  
 ===== Electric Field and Potential for Lines of Charge ===== ===== Electric Field and Potential for Lines of Charge =====
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 [{{  184_notes:dqandr.png?300|$dQ$ and $r$ for point P from a little bit charge along the line of tape}}] [{{  184_notes:dqandr.png?300|$dQ$ and $r$ for point P from a little bit charge along the line of tape}}]
  
-However, to make the best model of this line of charge, we would need to split the line into extremely small pieces of charge or infinitesimally small pieces of charge, which in calculus notation, we would write as dQ. We can then find the electric field at Point A due to only that small piece of charge - this would be "a little bit of electric field" since it comes from "a little bit of charge", so we would write this as dE. Now if we have an extremely small piece of a line of charge, this **__DOES__** look exactly like a point of charge. We know how to handle points of charge. [[184_notes:pc_efield|Using the equation for electric field of a point charge]], we can say that the little bit of electric field that comes from our little bit of charge would be:+However, to make the best model of this line of charge, we would need to split the line into extremely small pieces of charge or infinitesimally small pieces of charge, which in calculus notation, we would write as dQ. We can then find the electric field at Point A due to only that small piece of charge - this would be "a little bit of electric field" since it comes from "a little bit of charge", so we would write this as dE.// Now if we have an extremely small piece of a line of charge, this DOES look exactly like a point of charge.// We know how to handle points of charge. [[184_notes:pc_efield|Using the equation for electric field of a point charge]], we can say that the little bit of electric field that comes from our little bit of charge would be:
 $$\vec{dE}=\frac{1}{4\pi\epsilon_0}\frac{dQ}{r^2}\hat{r}=\frac{1}{4\pi\epsilon_0}\frac{dQ}{r^3}\vec{r}$$   $$\vec{dE}=\frac{1}{4\pi\epsilon_0}\frac{dQ}{r^2}\hat{r}=\frac{1}{4\pi\epsilon_0}\frac{dQ}{r^3}\vec{r}$$  
  
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