Calculating Magnetic Field Around Window Frame

[miggitymark]

Homework Statement

Sounds like the beginning to a bad joke right?

Two long straight wires pass through a window frame (1m x 1.5m). One wire carries 1A out of the room and one wire carries 8A in. Find magnitude of closed integral of vector B * vector dl around window frame.
Answer in Tesla*m

Homework Equations

B= mu*I / 2pi*r

The Attempt at a Solution

I don't know what the question is asking: What is this integral with a circle in it of the dot product of the B field and dl?

The wires have magnetic fields, they induce current through the window frame, which then has its own magnetic field. Is this what the questino is asking or does it want the field along the length of the edge if this frame?

thanks for reading

 

[LowlyPion]

Homework Statement

Sounds like the beginning to a bad joke right?

Two long straight wires pass through a window frame (1m x 1.5m). One wire carries 1A out of the room and one wire carries 8A in. Find magnitude of closed integral of vector B * vector dl around window frame.
Answer in Tesla*m

Homework Equations

B= mu*I / 2pi*r

The Attempt at a Solution

I don't know what the question is asking: What is this integral with a circle in it of the dot product of the B field and dl?

The wires have magnetic fields, they induce current through the window frame, which then has its own magnetic field. Is this what the questino is asking or does it want the field along the length of the edge if this frame?

thanks for reading

I think you are talking about the line integral about a closed path, which is represented as the integral symbol with an "o" in the middle.

As to the problem I think you want to be considering Ampere's law:
http://hyperphysics.phy-astr.gsu.edu/Hbase/magnetic/amplaw.html

 

[miggitymark]

YES! the line integral, which I have no idea what that is so I'm looking it up.

So using Ampere's law (which relates much better to this problem) I set up:

The window is 1.5m wide (X) and 1m tall (Y) and I is 7 Amps

B= 7*mu / 2X+2Y which equals 7mu / 5

So B = approximately 1.759e-6

Now, what is the "magnitude of the line integral of B*dl" and what does that mean? and more importantly, how does it relate to the answer I got?

Dimensional analysis tells me that Tesla-meters/Amps * Amps divided by meters (perimeter of window frame) comes out to Tesla-meters which is what they want, but the concepts of line integrals and dot products and vectors is unknown to me so the answer doesn't seem right.

 

[LowlyPion]

Here's another link that goes into more detail than you may want.

http://en.wikipedia.org/wiki/Ampère's_law