Magnetic Field of Two Wires where is zero

In summary, the magnetic field is zero at the location P on the y-axis where the current I1 = 49 A and I2 = 31 A are in opposite directions parallel to the x-axis.
  • #1
hellogirl88
15
0
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!
 
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  • #2
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 = μo*I/2π*R you need to construct an equation that describes where the fields are equal but opposite.
 
  • #3
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
 
  • #4
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
 
  • #5
LowlyPion said:
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?
 
  • #6
hellogirl88 said:
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.
 
  • #7
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?
 
  • #8
hellogirl88 said:
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.
 
  • #9
I finally got it. Thank you so much for your help
 

1. What is a magnetic field?

A magnetic field is a region in space where a magnetic force can be detected. It is created by moving electric charges and is represented by lines of force that indicate the direction and strength of the force.

2. How is the magnetic field of two wires calculated?

The magnetic field of two wires can be calculated using the Biot-Savart law, which states that the magnetic field at a point is directly proportional to the current in the wire, the distance from the wire, and the sine of the angle between the wire and the direction of the field.

3. Where is the zero point of the magnetic field in two wires?

The zero point of the magnetic field in two wires is the point where the magnetic field strength is equal to zero. This point is typically located at the midpoint between the two wires.

4. How does the direction of the current affect the magnetic field of two wires?

The direction of the current in the wires affects the direction of the magnetic field. If the current in both wires is in the same direction, the magnetic fields will add together and create a stronger field. If the currents are in opposite directions, the magnetic fields will cancel each other out and the resulting field will be weaker.

5. What is the significance of the zero point in the magnetic field of two wires?

The zero point of the magnetic field in two wires is important because it represents the point where the magnetic forces from the two wires are equal and opposite, resulting in a net force of zero. This point can be used to determine the location of objects in relation to the wires, as they will experience no magnetic force at this point.

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