Electric Field Intensity at a point due to a infinite line charge

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Homework Help Overview

The problem involves calculating the electric field intensity at a specific point due to infinite uniform line charges positioned along the x and y axes. The context is within electrostatics, specifically focusing on the effects of line charges in free space.

Discussion Character

  • Exploratory, Assumption checking, Mixed

Approaches and Questions Raised

  • Participants discuss the placement of the line charge and whether it lies in the z=0 plane. There are considerations about using Gauss's law versus other methods. Questions arise about whether to treat the contributions from the x-axis and y-axis line charges separately and how that affects the resulting expression.

Discussion Status

The discussion is ongoing, with participants exploring different methods to approach the problem. Some guidance has been offered regarding the use of superposition and the implications of evaluating the electric field at the specified point. There is a recognition that the field at the point of interest is a function of one coordinate but not the others.

Contextual Notes

Participants are navigating the constraints of the problem, including the requirement to find the electric field without relying on Gauss's law and the implications of the line charge configuration on the resulting calculations.

Abel I Daniel
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Homework Statement



Infinite uniform line charges of 5nc/m lie along the (positive and negative) x and y axes in free space.
Find E at :P(0,3,4)

Homework Equations


E due to line charge along the Z-axis is given by:
E=(λ/(2∏*ε*r))*ar
where λ=line charge density;ε= permitivity;r=radial distance of point from the line charge;ar=unit vector along the direction of E.


The Attempt at a Solution


Here the line charge lies in z=0 plane right??
 
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Abel I Daniel said:
Here the line charge lies in z=0 plane right??

Yes. Is that all you wanted to know?
 
ok,but I am trying to do without the help of Gauss law..
 
so,does it require to take both the cases(along x-axis and y-axis)individually and finally add them ??
If that is the method,we will get an expression of function of x and y(instead of a constant value) right?
 
Abel I Daniel said:
so,does it require to take both the cases(along x-axis and y-axis)individually and finally add them ??
If that is the method,we will get an expression of function of x and y(instead of a constant value) right?

No.
When evaluated at (0,3,4) it will be a constant. The method is immaterial to the answer.

Of course, the field at P(x0, y0, z0) is a function of z0 but not of x0 or y0.
 

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