What is the magnetic field due to a ribbon of current-carrying wires?

[samjohnny]

Homework Statement

Attached.

Homework Equations

The Attempt at a Solution

I've been meaning to do this question for a while now but don't have much of a strategy. I was informed that the ribbon should be treated as a series of parallel wires. The magnetic field at an arbitrary point P from a wire with a current flowing through it can be given by the biot-savart law. The magnetic field at a point P a distance r away from a single long wire is thus given by:

Now, I have the suspicion that, since the ribbon comprises a whole bunch of wires, the total magnetic field due to the ribbon would simply be the result of an integration over the width of the ribbon. However I am having difficulty in figuring out the initial set up of the integral., and an appropriate parameterisation (if that is at all needed).

 

[mfb]

Now, I have the suspicion that, since the ribbon comprises a whole bunch of wires, the total magnetic field due to the ribbon would simply be the result of an integration over the width of the ribbon.

Right.

Which distances do the "parallel wires" have from P? What would you integrate over?

 

[samjohnny]

Right.

Which distances do the "parallel wires" have from P? What would you integrate over?

Well, from the diagram it'd seem that the bottom of the ribbon is R+(w/2) from P, and that R-(w/2) is the distance between P and the top of the ribbon. Would it then be a matter of using these as the limits of integration?

 

[mfb]

Would it then be a matter of using these as the limits of integration?

Right.