Current on Parallel Conducting Wires

[aglo6509]

Homework Statement

Two very long, straight, parallel wires carry currents that are directed perpendicular to the page as shown in Figure P30.9. Wire 1 carries a current I1 into the page (in the -z direction) and passes through the x-axis at x = +a. Wire 2 passes through the x-axis at x = -2a and carries an unknown current I2. The total magnetic field at the origin due to the current-carrying wires has the magnitude 2µ0I1 / ( 2πa ). The current I2 can have either of two possible values.

Diagram: http://www.webassign.net/serpop/p22-29.gif

Homework Equations

The Attempt at a Solution

I needed to get this online homework done fast so I had to look up the answers and got I2 = 2*I1 and I2 = 6*I1. These were right but I have no idea how to get them and i struggled with this for about an hour now and still nothing. In my textbook also it only shows how to find the force between them. Its driving me nuts to figure this out and could really use some help on this one.

 

[vela]

The field at the origin is simply the vector sum of the individual fields due to wire 1 and wire 2.

What's the field at the origin due to wire 1, magnitude and direction?

What's the total field at the origin?

 

[aglo6509]

The field at the origin is simply the vector sum of the individual fields due to wire 1 and wire 2.

What's the field at the origin due to wire 1, magnitude and direction?

Wouldn't it just be µI2/(2πa) ?

 

[vela]

Why would it depend on I₂ if it's the field due to wire 1? And in what direction does the field point?

 

[aglo6509]

Oh yeah I was trying to find I2, so would it be µI1/2πa and pointing out of the page because of the right hand rule?

 

[vela]

You do want to use the right hand rule, but it doesn't point out of the page. Remember the field lines form circles centered on the wire, so the field will lie in the plane of the page.

 

[aglo6509]

Ohh okay so it would make a Clockwise B- field?

 

[vela]

Yup, so at the origin, the field due to wire 1 points up the page.

 

[aglo6509]

Okay so how have I make that forumla condense down too I2 = 2*I1?

 

[vela]

Apply what I said in post 2. You need to figure this out on your own.