Magnetic field of current ribbon

[levicivita]

Homework Statement

Hello,

I'm wondering what is the best way to go about calculating the magnetic field generated by an infinite current ribbon of width 2units, with current j = exp(wti), w = omega, t = time. The wavelength associated with the oscillation is 1unit.

The Attempt at a Solution

My current method would be to calculate the magnetic field due to an infinite wire with the same current, and integrate to get that for the entire ribbon. However, I am given the x-component of the magnetic field, which is in the form of a Fourier integral - so I'm wondering if there is an easier alternative method (as this seems to suggest), and if I can derive the y-component in a similar fashion.

I think part of the reason why I am struggling with this is because the problem is expressed in complex exponentials, so if anyone can shed some light on this I would really appreciate it!

 

[NateD]

The best way to calculate the magnetic field generated by an infinite current ribbon of width 2 units with a current of j = exp(wti), w = omega, t = time is to use Biot-Savart's law and integrate over the entire length of the ribbon. This will give you the total magnetic field generated by the ribbon. The x-component of the magnetic field can then be found using the Fourier integral representation of the current. The y-component of the magnetic field can be found by using a similar method.