Alculate the x-component of the electric field

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Homework Statement


Positive charge Q is distributed uniformly along the positive y-axis between y=0 and y=a . A negative point charge −q lies on the positive x-axis, a distance x from the origin

Calculate the x-component of the electric field produced by the charge distribution Q at points on the positive x-axis.

Calculate the y-component of the electric field produced by the charge distribution Q at points on the positive x-axis.

Homework Equations


E = q/4πε0r2
r2 = x2+y2

The Attempt at a Solution


So I was able to get the first part of the question relatively easily by using some techniques from the textbook, which resulted in the correct answer:

dEx = Q/4πε0x√(x2+a2)

But when I try to find the y-component, I get the answer:

dEy = (Q/(8πε0a))*(1-(x/(√x2+a2)))

This answer results in the following message from the website:
"Your answer either contains an incorrect numerical multiplier or is missing one."

I need help finding the problem since I don't know where I may have gone wrong.
 

Answers and Replies

  • #2
Nathanael
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Calculate the x-component of the electric field produced by the charge distribution Q at points on the positive x-axis.

Calculate the y-component of the electric field produced by the charge distribution Q at points on the positive x-axis.
Just making sure; do you mean, "on the positive y-axis"?

dEx = Q/4πε0x√(x2+a2)
This gave you the correct answer? The units are incorrect. It might be simply a typo (because it's almost correct) but I want to make sure you understand how to do this before finding the y-component.

Edit:
The units are correct sorry... I misread the equation
 
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  • #3
haruspex
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This gave you the correct answer? The units are incorrect.
Assuming it is intended as Ex = Q/(4πε0x√(x2+a2)), the dimensions are correct (but yes, the expression is wrong... it should not tend to infinity as x tends to zero).
 
  • #4
haruspex
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But when I try to find the y-component, I get the answer:
You don't say how you got that answer. We can't tell you where you went wrong if you don't post your working/logic.
 
  • #5
rude man
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Homework Statement


Positive charge Q is distributed uniformly along the positive y-axis between y=0 and y=a . A negative point charge −q lies on the positive x-axis, a distance x from the origin

Calculate the x-component of the electric field produced by the charge distribution Q at points on the positive x-axis.

Calculate the y-component of the electric field produced by the charge distribution Q at points on the positive x-axis.

Homework Equations


E = q/4πε0r2
r2 = x2+y2

The Attempt at a Solution


So I was able to get the first part of the question relatively easily by using some techniques from the textbook, which resulted in the correct answer:

dEx = Q/4πε0x√(x2+a2)
As pointed out in post #2, this answer is incorrect. Did you do a typo somewhere? And why "dEx"? It's just Ex.
You should be figuring the problem out for yourself rather than looking for formulas in a textbook.
If you did that you would have come up with one definite integral over y=0 to y=a for the x component, and a different definite integral, also over y=0 to y=a, for the y component.
BTW why is q mentioned in the problem?
Also, both the x and y components of the E field are obviously negative for all x. The answers have to be sign-reversed in x for x < 0.
 
  • #6
haruspex
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BTW why is q mentioned in the problem?
Most likely for a later part of the question.
 

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