What is the Electric Field at P(0,0,4)?

Click For Summary
SUMMARY

The discussion focuses on calculating the electric field at point P(0,0,4) due to infinite line charges of 5nC/m located along the x and y axes. The relevant equation used is E = (pl/2(pi)(eo)p)ap, where pl is the line charge density, eo is the permittivity of free space (8.854 x 10^-12), and ap is the unit vector. The final answer for the electric field at point P is determined to be 45az, derived through symmetry considerations that simplify the problem to a single effective line charge with a density of 10nC/m.

PREREQUISITES
  • Understanding of electric field concepts and calculations
  • Familiarity with line charge density and its implications
  • Knowledge of vector calculus, particularly unit vectors
  • Basic grasp of electrostatics and symmetry in electric fields
NEXT STEPS
  • Study the derivation of electric fields from line charges using the formula E = (pl/2(pi)(eo)p)ap
  • Learn about the concept of superposition in electric fields
  • Explore the implications of symmetry in electrostatics
  • Investigate the properties of the permittivity of free space (eo) and its role in electric field calculations
USEFUL FOR

This discussion is beneficial for physics students, electrical engineering majors, and anyone studying electrostatics or electric field calculations involving line charges.

LeeroyJenkins
Messages
8
Reaction score
0

Homework Statement


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


Homework Equations


E = (pl/2(pi)(eo)p)ap
pi = 3.14...
eo - permitivity of free space 8.854 x 10^-12
pl = line charge density
ap = unit vector

The Attempt at a Solution


really just need to know how to solve for the unit vector pl then I can do the rest.
I was thinking along the lines of ap = (z-4) az/ sqrt((z-4)^2) then plug in z... not really sure. Any help would be appreciated.

The answer is 45az but how?
 
Physics news on Phys.org
Why the unit vector pl?

Through symmetry (You're on the z-axis) isn't the set up equivalent to just a single line charge with density 10 taken from the radius of 4?
 

Similar threads

Find the electric field of a long line charge at a radial distance
  • · Replies 1 ·
Replies
1
Views
2K
Electric field due to charges between 2 parallel infinite planes
  • · Replies 9 ·
Replies
9
Views
2K
Not necessarily homework help but I do not understand Field lines
  • · Replies 2 ·
Replies
2
Views
1K
Electric Field Intensity at a point due to a infinite line charge
  • · Replies 5 ·
Replies
5
Views
8K
Electric Field of two line charges
  • · Replies 3 ·
Replies
3
Views
1K
Electric field at a point within a charged circular ring
  • · Replies 68 ·
3
Replies
68
Views
8K
Find the electric field intensity from an infinite line charge
  • · Replies 3 ·
Replies
3
Views
2K
Why is electric field at the center of a charged disk not zero?
  • · Replies 4 ·
Replies
4
Views
4K
Electricity and magnetism: Electric Field for Two Long Charged Lines
  • · Replies 1 ·
Replies
1
Views
1K
Finding E Field at Point from non uniform charge density
  • · Replies 5 ·
Replies
5
Views
2K