# Calculate magnetic field intensity

DODGEVIPER13

## 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)

∫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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## Homework Statement

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

Figure 1?

DODGEVIPER13
whoops I was tired and forgot to add it

#### Attachments

• Homework 3.pdf
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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:
DODGEVIPER13
(x1,y1,z1)-(x2,y2,z2)=(x1-x2,y1-y2,z1-z2) then Ry=(0,0,0)-(0,4,0)=(0,-4,0)

DODGEVIPER13
right or no? I think that is what I did earlier uggg

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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.

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(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).

DODGEVIPER13
well I found a thing on euclidean distance Ry=sqrt((0-0)^2+(0-4)^2+(0-0)^2)=4

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well I found a thing on euclidean distance Ry=sqrt((0-0)^2+(0-4)^2+(0-0)^2)=4

Much better.

DODGEVIPER13
Ok so then Rz=sqrt((0,0,0)^2-(0,0,4)^2)=4 right?

DODGEVIPER13
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?

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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.

DODGEVIPER13
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

DODGEVIPER13
H=H1+H2=(10/2(pi)4)-(10/2(pi)4)=0

DODGEVIPER13
That doesn't seem right?

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Ok so then Rz=sqrt((0,0,0)^2-(0,0,4)^2)=4 right?

Right.

DODGEVIPER13
Ok well now that my distances are confirmed correct is my new answer correct?

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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.

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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.

DODGEVIPER13
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.

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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.

DODGEVIPER13
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?

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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?

DODGEVIPER13
well since H is the magnetic field strength then it should turn in the same direction as the B field right so wouldnt it point in the same direction as the B field im confused?

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well since H is the magnetic field strength then it should turn in the same direction as the B field right so wouldnt it point in the same direction as the B field im 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.

DODGEVIPER13
well the one going into the page is curling up so it is in the direction of the z-axis?

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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?

DODGEVIPER13
the -Z direction so -k

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the -Z direction so -k

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

DODGEVIPER13
I guess I used RHR wrong the second time would it be +Z again or is it on the Y-axis? Is there an easier way for me to see this?

DODGEVIPER13
would it be in the direction of the Y-axis?

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would it be in the direction of the Y-axis?

Possibly. Which direction, +y or -y?

DODGEVIPER13
+y heh I am just guessing based on RHR

DODGEVIPER13
Well I think I found and appropriate equation setup for the into the page part H=I/2(pi)rho=(5/(pi)(4))k