Find the electric field intensity from an infinite line charge

In summary, I have determined the vector between the point (4, 0, 0) and the point P. The norm of this vector is the radial distance of the line to point P (the value of “ρ” in the formula) and its unit vector is the direction of the electric field.
  • #1
math132003
3
1
Homework Statement
Consider that in an rectangular coordinate system an infinite charge line is placed exactly on the "x" axis. This line has a uniform charge distribution with linear charge density pL = 10 nC/m

(a) Determine the electric field intensity vector at point P = (4, 6, 8)

(b) What is the point charge value that should be placed at the point (0, -6, 8) so that the component of the Ey field at the same point P is null.
Relevant Equations
Electric field due to infinite line of charge, E = (pL/(2pi*r*p))*âp
what I've done so far?

-i've determined the vector between the point (4, 0, 0) and the point P.
(4, 6, 8) - (4, 0, 0)
(0, 6, 8)

-The norm of this vector is the radial distance of the line to point P (the value of “ρ” in the formula)
√(0^2 + 6^2 + 8^2) = 10 -> ρ = 10

-and its unit vector is the direction of the electric field (it is the unit vector âρ in the formula)
(1/10)*(0,6,8) -> (0, 3/5, 4/5)how can i continue?
Thanks in advance!
 
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  • #2
Hello @math132003. :welcome: !

If I translate your notation to the hyperphysics notation: $$E = {\lambda\over 2\pi \,r\,\varepsilon_0}
$$pL ##\qquad## is ##\qquad\lambda##
##\rho \qquad\ ## is ##\qquad## r
p ##\qquad## is ##\qquad\varepsilon_0##
And you use âp in the formula, but then write âρ in the comment

Confuses me somewhat -- please explain.

In the mean time I continue in the hyperphysics notation, adding a radial unit vector ##\hat r## in the ##yz## plane, so that
$$\vec E = {\lambda\over 2\pi \,r\,\varepsilon_0}\,\hat r
$$for which you have ##r = 10## and ##\hat r = (0, 3/5,4/5)##.

So what's the problem ?
 
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  • #3
Hello @BvU!

Thanks for the translation and I apologize for the confusion. Langauge problems. :oldbiggrin:

Even knowing this expression i still can't go ahead and develop these items:

(a) Determine the electric field intensity vector at point P = (4, 6, 8)

* here I just need to take everything I found and replace in the expression above? (b) What is the point charge value that should be placed at the point (0, -6, 8) so that the component of the Ey field at the same point P is null.

* I still don't know how to do anything on that item

Thank you again.
 
  • #4
math132003 said:
* here I just need to take everything I found and replace in the expression above?
Yes! And carefully check your answer (including units !)

(b) For this you need a formula for the electric field of a point charge Q. I don't spoil the exrcise if I tell you that the formula is$$\vec E = {Q\over 4\pi\,r^2\varepsilon_0}\hat r$$ where ##\vec r## is pointing from ##(0,-6,8)## to P. Your job to find the length and the ##y## component.
A sketch in the plane containing the ##x## axis and P might help.
 
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Related to Find the electric field intensity from an infinite line charge

1. How is the electric field intensity calculated from an infinite line charge?

The electric field intensity from an infinite line charge is calculated using the formula E = λ / (2πεr), where λ is the linear charge density, ε is the permittivity of the medium, and r is the distance from the line charge.

2. What is the direction of the electric field from an infinite line charge?

The electric field from an infinite line charge is always perpendicular to the line charge and points away from it.

3. How does the electric field change as the distance from the line charge increases?

The electric field from an infinite line charge decreases as the distance from the line charge increases. This is because the field spreads out over a larger area as the distance increases.

4. Can the electric field from an infinite line charge be negative?

Yes, the electric field from an infinite line charge can be negative. This occurs when the line charge has a negative linear charge density, which means the electric field points towards the line charge instead of away from it.

5. How does the electric field from an infinite line charge compare to that of a point charge?

The electric field from an infinite line charge is similar to that of a point charge, except that the field is uniform along the entire length of the line charge. In contrast, the electric field from a point charge decreases as the distance from the point charge increases.

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