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

AI Thread Summary
The discussion revolves around calculating the electric field at x=4µm using the potential function V(x) = 20/(x^2-4)V. The electric field E is derived from the potential using the equation E = -∂V/∂x. The user successfully differentiates the potential to find E_x = 40x/(x^2-4)^2. The final step involves substituting x=4 into the derived expression, resulting in E_x = 10/9 V/µm. The process and application of the quotient rule in differentiation are clarified during the discussion.
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?
 
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Likes gracy
blue_leaf77 said:
right?
Yes,of course.
 
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