Electric Field at a Point on the x-Axis Due to Charges

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Homework Help Overview

The problem involves calculating the electric field at a specific point on the x-axis due to a potential function derived from charges. The potential is given as V(x) = 20/(x² - 4) V, and the electric field is related to the potential through the derivative with respect to x.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to differentiate the potential function to find the electric field but expresses confusion about the steps involved in the differentiation process.
  • Some participants reference external resources, such as the quotient rule, to clarify the differentiation method.
  • There is a question about how to evaluate the derived expression for the electric field at the specific point x = 4 µm.

Discussion Status

The discussion is ongoing, with participants providing references and confirming steps in the differentiation process. There is an indication of collaborative exploration of the problem, but no consensus has been reached regarding the understanding of the differentiation steps.

Contextual Notes

The original poster has indicated they have a solution but are struggling with understanding the differentiation process. The problem context involves specific values and the application of calculus to find the electric field from the potential function.

gracy
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Homework Statement


The potential at a point x(measured in µm)due to some charges situated on the x-axis is given by ##V(x)##=##\frac{20}{x^2-4}##V.The electric field ##E## at x=4µm is ?

Homework Equations


##E##=-##\frac{∂V}{∂r}##

The Attempt at a Solution


Actually I have solution but still I am unable to understand.So ,instead of my attempt at a solution .I 'll post solution itself.
##Ex##=-##\frac{∂V}{∂x}## (1)

= -##\frac{d}{dx}(\frac{20}{x^2-4})## (2)

=##\frac{40x}{(x^2-4)^2}## (3)

##Ex## at x=4µm =##\frac{10}{9}##V/µm
Here I am not able to understand how it proceeded from (2) to (3)
 
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And how to proceed from (3) to answer?
 
You just plug in x=4 into the expression, right?
 
  • Like
Likes   Reactions: gracy
blue_leaf77 said:
right?
Yes,of course.
 

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