Calculate magnetic field intensity

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Discussion Overview

The discussion revolves around calculating the magnetic field intensity (H) generated by two infinitely long parallel filaments. Participants explore the application of Ampere's law and the geometric considerations necessary for determining H at specific points in space, particularly at the origin and at the coordinates (-1,2,2).

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant attempts to apply Ampere's law to find H at the origin and at (-1,2,2), using the equation H=H1+H2.
  • Another participant points out the need to consider the signs of the enclosed currents, which flow in opposite directions.
  • There is confusion regarding the correct computation of distances Ry and Rz, with multiple participants providing differing interpretations and corrections.
  • Participants discuss the direction of the magnetic field and the application of the right-hand rule (RHR) to determine the orientation of H at the origin.
  • One participant proposes that the H field should point in the same direction as the B field, leading to further discussion about the correct application of the RHR.
  • There is a suggestion to express the final answer in terms of unit vectors, and a participant questions whether to include units or present the answer in phasor form.
  • Another participant raises the question of whether the x-component of the observation point affects the calculation of H, leading to further exploration of the geometry involved.

Areas of Agreement / Disagreement

Participants express differing views on the correct computation of distances and the application of the right-hand rule. There is no consensus on the final answers for both parts of the problem, and the discussion remains unresolved regarding the implications of the x-component of the observation point.

Contextual Notes

Participants have noted limitations in their understanding of the geometry involved in calculating distances and the direction of the magnetic field. There are unresolved questions about the impact of the x-component on the magnetic field calculations.

DODGEVIPER13
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Homework Statement


Two infinitely long filaments are placed parallel to the x-axis as shown in Figure 1.
a)Find H at the origin
b)Find H at (-1,2,2)


Homework Equations


∫Hdl=Ienclosed
H=H1+H2

The Attempt at a Solution


Well following the equation above I get Hl= Ienc then H1=Ienc/(2piRy) and H2=Ienc/(2piRz) then Ry=(0,0,0)-(0,4,0)=(0,-4,0) then length of Ry=4 and Rz=(0,0,0)-(0,0,4)=(0,0,-4) then Rz=4 thus H1=Ienc/(8pi) and H2=Ienc/(8pi) then H=H1+H2=10/(8pi)+10/(8pi)=20/(8pi)=.795 A/m that is for part a) I only listed this as I used the same method for part b) just with (-1,2,2) instead of (0,0,0)
 
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DODGEVIPER13 said:

Homework Statement


Two infinitely long filaments are placed parallel to the x-axis as shown in Figure 1.

Figure 1?
 
whoops I was tired and forgot to add it
 

Attachments

Use Ampere's law: ∫H*ds = i. Which you did, sort of.

What you failed to do was to
(1) pay attention to the signs of Ienc y and Ienc z. The two currents are in opposite directions.

(2) compute Ry and Rz correctly. Given two points (x1 y1 z1) and (x2 y2 z2) what is the distance between them?
 
Last edited:
(x1,y1,z1)-(x2,y2,z2)=(x1-x2,y1-y2,z1-z2) then Ry=(0,0,0)-(0,4,0)=(0,-4,0)
 
right or no? I think that is what I did earlier uggg
 
DODGEVIPER13 said:
right or no? I think that is what I did earlier uggg

That's what you did, and it's wrong.

Check your analytic geometry text or the Web.
 
DODGEVIPER13 said:
(x1,y1,z1)-(x2,y2,z2)=(x1-x2,y1-y2,z1-z2) then Ry=(0,0,0)-(0,4,0)=(0,-4,0)

That's wrong. Furthermore, Ry is a distance and cannot be described by (x,y,z).
 
well I found a thing on euclidean distance Ry=sqrt((0-0)^2+(0-4)^2+(0-0)^2)=4
 
  • #10
DODGEVIPER13 said:
well I found a thing on euclidean distance Ry=sqrt((0-0)^2+(0-4)^2+(0-0)^2)=4

Much better.
 
  • #11
Ok so then Rz=sqrt((0,0,0)^2-(0,0,4)^2)=4 right?
 
  • #12
Ah the directions are different one in into the page and one is out. I can't remember does x mean into the page or out of the page?
 
  • #13
DODGEVIPER13 said:
Ah the directions are different one in into the page and one is out. I can't remember does x mean into the page or out of the page?

x is into the page and . is out of the page.
 
  • #14
Ok so on the current is clockwise and on the dot current is counter clockwise so in the z direction it is negative and y it is positive
 
  • #15
H=H1+H2=(10/2(pi)4)-(10/2(pi)4)=0
 
  • #16
That doesn't seem right?
 
  • #17
DODGEVIPER13 said:
Ok so then Rz=sqrt((0,0,0)^2-(0,0,4)^2)=4 right?

Right.
 
  • #18
Ok well now that my distances are confirmed correct is my new answer correct?
 
  • #19
DODGEVIPER13 said:
Ok so on the current is clockwise and on the dot current is counter clockwise so in the z direction it is negative and y it is positive

Currents don't run in circles. Currents run in the wires which are straight.
 
  • #20
DODGEVIPER13 said:
H=H1+H2=(10/2(pi)4)-(10/2(pi)4)=0

No.
H is a vector, that's why I use bold type for it.

Take one wire at a time and determine the direction of H for it using your pix. You have the magnitudes right.
 
  • #21
well it seems to be flowing into the page on the y-axis and out of the page on the z axis. So on the y-axis the H vector would go left. Then I am guessing on the z axis since they are opposite the other H field must be to the right.
 
  • #22
DODGEVIPER13 said:
well it seems to be flowing into the page on the y-axis and out of the page on the z axis. So on the y-axis the H vector would go left. Then I am guessing on the z axis since they are opposite the other H field must be to the right.

Why left on the z axis? Do you know the right-hand rule?
Same comment for the z wire.
Draw circles around each wire intersecting with the origin, then use the rt-hand rule.
 
  • #23
Well for the one into the page the B field will rotate clockwise and out of the page the B field will go counterclockwise. I said left and right because you have said something about the wires being straight and not circular so I guess I did not understand what you meant?
 
  • #24
DODGEVIPER13 said:
Well for the one into the page the B field will rotate clockwise and out of the page the B field will go counterclockwise.

That is correct. So, taking the one into the page first, what direction does the H field point at the origin?
 
  • #25
well since H is the magnetic field strength then it should turn in the same direction as the B field right so wouldn't it point in the same direction as the B field I am confused?
 
  • #26
DODGEVIPER13 said:
well since H is the magnetic field strength then it should turn in the same direction as the B field right so wouldn't it point in the same direction as the B field I am confused?

Yes, same direction as the B field. Which direction is that? I need it in terms of unit vectors or at least a verbal description.
 
  • #27
well the one going into the page is curling up so it is in the direction of the z-axis?
 
  • #28
DODGEVIPER13 said:
well the one going into the page is curling up so it is in the direction of the z-axis?

YES! The +z direction, let's call it +k, k the unit vector along the z axis.

Now, the other one?
 
  • #29
the -Z direction so -k
 
  • #30
DODGEVIPER13 said:
the -Z direction so -k

No. Look more carefully at the H circle where it intersects with the origin.
 

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