The current density inside a long, solid, cylindrical wire of radius a = 10 cm is in the direction of the axis and varies linearly with the radial distance r cm from the axis according to J = J(adsbygoogle = window.adsbygoogle || []).push({}); _{0}r / a with J_{0}=0.5 A/cm^{2}. Find the magnetic field in μT at r = 0.045 m

Ok I know from amperes law that the magnetic field in this case can be derived to be:

B=(mew_{0}/2*pi)(I*r/R^{2})

Edit: Wait.. Is that above equation right? That might have been what I did wrong.. When I worked it out I used B= (mew_{0}*I) / (2*pi*r)

Was that my mistake?

Since it says J = J_{0}r / a

And I know current density is I=J*A where A is area

I put those two equations together. Since there is no length of the wire, for Area I just used pi*r^2

J = J_{0}*r(pi*r^2) / a

Where r=.045m, a=10cm, and J_{0}=0.5 A/cm^{2}

Not sure if I have interpreted the question correctly, or if that is the right way to do it.. From there I just put that in as I into the original magnetic field equation, using r on the bottom once again as .045m to get my answer. It was still wrong. Thats my attemp, what did I do wrong?

I converted everything to SI units, to convert A/cm^2 to A/m^2 I multiplied it by 10,000. Is that right?

Anyone know how to get this?

Thanks.

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# Ampere's Law and current density

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