Magnetic Field of Two Wires where is zero

[hellogirl88]

Two wires carry current I1 = 49 A and I2 = 31 A in the opposite directions parallel to the x-axis at y1 = 7 cm and y2 = 15 cm. Where on the y-axis (in cm) is the magnetic field zero?


I don't even know where to start on this. Any help would be great!

 

[LowlyPion]

Consider the magnetic field of a wire carrying current:
where (+) is going into the page, and (.) is coming up out of the page.

(+) (+) (+) (+) (+) (+)
------------------------>
(.) (.) (.) (.) (.) (.)

If you add one going the other direction then:

(+) (+) (+) (+) (+) (+)
------------------------>
(.) (.) (.) (.) (.) (.)

(.) (.) (.) (.) (.) (.)
<------------------------
(+) (+) (+) (+) (+) (+)

So in between the fields reinforce. Which means to either side they may cancel somewhere - which is what you want.

With the B field given by B = μ_o*I/2π*R you need to construct an equation that describes where the fields are equal but opposite.

 

[hellogirl88]

Well originally I was thinking μo*I1/2π*R = - μo*I2/2π*R, but I know this is wrong. Then I considered I1/R1 = - I2/R2, but I don't think this is right either...so I am still lost

 

[LowlyPion]

You need to pick some location call it P outside the 2 wires. It will be a distance of D away from one wire and D + 8 cm away from the other. Now what you need to do is find where the fields are equal.

Use that in your I1/R1 = I2/R2

 

[hellogirl88]

You need to pick some location call it P outside the 2 wires. It will be a distance of D away from one wire and D + 8 cm away from the other. Now what you need to do is find where the fields are equal.

Use that in your I1/R1 = I2/R2

So say I pick P as Y = 17, so that point would be 2cm away from wire 1 and 10 cm away from wire 2...how do I use this information to find where the fields are equal?

 

[LowlyPion]

So say I pick P as Y = 17, so that point would be 2cm away from wire 1 and 10 cm away from wire 2...how do I use this information to find where the fields are equal?

No, no, no.

Say you pick R1 as D and R2 as 8 cm + D, and then solve for what D is.

 

[hellogirl88]

Ok, so I did 49/D = 31/D+8 and solved for D...is this value supposed to be where on the Y axis the magnetic field is zero?

 

[LowlyPion]

Ok, so I did 49/D = 31/D+8 and solved for D...is this value supposed to be where on the Y axis the magnetic field is zero?

It's not the Y coordinate value. It's the distance from the 49A laden wire. You will have to make a drawing and determine what that y coordinate value would be.

Note: Since you chose D as from the 49 you should expect that the (-) value you get is in the direction of the 31A wire and to the other side of it.

 

[hellogirl88]

I finally got it. Thank you so much for your help