E = -grad V, graphing!

  • Thread starter flyingpig
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  • #1
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Homework Statement




An electric field in a region of space is parallel to the x axis. The electric potential varies with position as shown in Figure P25.36. Graph the x component of the electric field versus position in this region of space.


[PLAIN]http://img841.imageshack.us/img841/2959/81320259.jpg [Broken]



The Attempt at a Solution



[PLAIN]http://img80.imageshack.us/img80/3752/13833299.jpg [Broken]

The green is the -grad V or just -dV/dx, at x = 2 to 3, I am just wondering, that is 0, but should I put a dot on the origin?
 
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Answers and Replies

  • #2
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Almost certainly. A graph like this should be continuous throughout (as long as you have all the data necessary to supply the points).

You may also want to consider how other people draw "square waves". Here is an example:

http://www.fourieroptics.org.uk/orgsq.png
 
  • #3
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It's a piecewise function...?
 
  • #4
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Ah ok, I see that the last part of my post wasn't concise.

I was trying to push you towards a way in which you may wish to draw your graph of E so that it would be more acceptable.

But yes you are correct, both the figure P25.36 and the one you have been asked to draw are piecewise functions.
 
  • #5
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Actually I just realize something, should I draw holes at the cusps?
 
  • #6
SammyS
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Actually I just realize something, should I draw holes at the cusps?
You definitely should!
 
  • #7
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You definitely should!

At x= 2 and 3, are those classified as cusps too? They look sharp...
 
  • #8
SammyS
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At x= 2 and 3, are those classified as cusps too? They look sharp...
Yes. dV/dx is discontinuous at those points.
 

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