# Homework Help: Magnetic field due to ribbon

1. Mar 13, 2015

### samjohnny

1. The problem statement, all variables and given/known data

Attached.

2. Relevant equations

3. 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).

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• ###### Magnetic field ribbon.JPG
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2. Mar 14, 2015

### Staff: Mentor

Right.

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

3. Mar 15, 2015

### samjohnny

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?

4. Mar 15, 2015

Right.