Integrating a charge along a line

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Homework Help Overview

The problem involves calculating the electric potential and electric field due to a uniformly distributed charge along a line segment. The total charge of 200 nC is spread from x = -100 mm to x = +100 mm, and the tasks include deriving the potential due to small charge elements, integrating to find the total potential as a function of y, and determining the conditions for maximum electric field strength.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to understand how to express the differential potential dV caused by each differential charge dQ and how to incorporate the variable y into the equations. Some participants suggest using the relationship dQ = λ dx and integrating over the specified limits to find the total potential. Questions arise regarding the role of the distance y in the calculations and how it relates to the integration process.

Discussion Status

Participants are actively engaging with the problem, clarifying the relationships between the variables involved. Some guidance has been provided regarding the integration process and the expression for r, but there is still uncertainty about how to properly incorporate y into the equations and the implications of the distance in the context of the problem.

Contextual Notes

There appears to be some confusion regarding the definitions and relationships between the variables, particularly how y is integrated into the calculations for electric potential and field. The original poster expresses difficulty in starting the problem, indicating a need for further clarification on these concepts.

burns12
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Homework Statement



total charge Q = 200[nC] is spread along a line from x=−100[mm] to x=+100[mm] .
a) write the dV caused by each dQ=λ dx .
b) integrate along the line of charge ; write V as a function of y .
c) take the derivative with y , to obtain that component of the Electric (vector) field .
d) take the derivative with y , again , to find where (along y-axis) the Ey is maximum


Homework Equations


We've used potential energy U=1/2QV...V=kQ/r...that's about it.


The Attempt at a Solution


What I can't get started with is the writing dV caused by each dQ. I'm not even sure what that means. And how can I write V as a function of y and take its derivative if there are no y's in any of these equations?

Any guidance here would be awesome, thanks
 
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hi burns12, welcome to PF.
Take a small element dx at a distance x from the origin.
Consider a point P at a distance y from the origin along y-axis.
Charge dq in the dx element is λ*dx, where λ = Q/L.
As you have mentioned
dV = k*dq/r. Put the value of dq and r.
To find V at P, take the integration between the limits x = -0.1 m to 0.1 m.
 
Thanks!

Ok so, the y comes into play as a distance on the y-axis that this dq charge is going to affect?
And do I integrate the dV = k*dq/r ? Or do I sub in λdx for dq and then integrate with respect to x to find dV?
I'm still not sure where this distance y would come into this.
 
burns12 said:
Thanks!

Ok so, the y comes into play as a distance on the y-axis that this dq charge is going to affect?
And do I integrate the dV = k*dq/r ? Or do I sub in λdx for dq and then integrate with respect to x to find dV?
I'm still not sure where this distance y would come into this.
dq = λ*dx and r = sqrt( x^2 + y^2)
 
Alright awesome I think I got it. Is the r = to sqrt(x^2 +y^2) because it's like the components of r in a sense?
 
burns12 said:
Alright awesome I think I got it. Is the r = to sqrt(x^2 +y^2) because it's like the components of r in a sense?
Yes.
 
Awesome, thanks for your help, that had me stumped for 2 days now ha
 

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