Calculating Electric Field at the Midpoint of a Charged Rod

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SUMMARY

The discussion centers on calculating the electric field at the midpoint of a uniformly charged rod of length L. The participant used the equation dE = K dq/r², where dq = Q/L dx, and integrated from -L/2 to L/2. The resulting expression for the electric field was E = -4KQ/L², which contradicted the expectation that the electric field at the midpoint should be zero. The error identified was the miscalculation of the distance r in the dE expression, which should account for the varying distances from the test charge to each charge element along the rod.

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madah12
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Homework Statement



let say we have a positively charged rod with length L then what is the electrical field at the middle point of the rod


Homework Equations





The Attempt at a Solution


I put the origin at the middle point
so dE=Kdq/r^2, dq = Q/L dx
E= kQ/L integral from -L/2 to L/2 (1/x^2)dx
=-KQ/L[2/L +2/L] =KQ/L (4/L) =-4KQ/L^2

well I expected it to be zero and it wasn't so should it be if so then what did I do wrong?
 
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The electric field is defined as [tex]\mathbf{E} = \displaystyle \lim_{q_0 \to 0} \frac{\mathbf{F}}{q_0}[/tex].

The r2 term in the expression for dE is the distance between some charge element dQ and this test charge q0. You didn't take this into account in your setup.
 
well my test charge q_0 is at the mid point of the rod and so is my origin so the distance between it and any other charge is x.
 

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