(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

magnetic field is azimuthal B(r) = B(p,z)[tex]\phi[/tex]

current density J(r) = Jp(p,z)p+ Jz(p,z)z

= p*exp[-p]p+ (p-2)*z*exp[-p]z

use stokes theorem to find B-filed induced by current everywhere in space

2. Relevant equations

stokes - {integral}dS.[curl A] = {closed integral}dl.A

curl B(r) = J(r)

3. The attempt at a solution

={integral}dS.[curl B(r)] = {closed integral}dl.B(r)

={integral}dS.J(r) = {closed integral}dl.B(p,z)[tex]\phi[/tex]

{integral}dS.J(r) = {integral}dS.p*exp[-p]p+ (p-2)*z*exp[-p]z= {closed integral}dl.B(p,z)[tex]\phi[/tex]

dl = pd[tex]\phi[/tex][tex]\phi[/tex]

dS = pd[tex]\phi[/tex]dzp+ pd[tex]\phi[/tex]dpz

So:

{closed integral}pd[tex]\phi[/tex].B(p,z)[tex]\phi[/tex]- with limits 0-2pi

= B(p,z)*2pi*p

{integral}dS.p*exp[-p]p+ (p-2)*z*exp[-p]z

do in 2 parts:

{integral}pd[tex]\phi[/tex]dz.p*exp[-p]p- with limits 0-2pi and 0-R

= 2pi*p^{2}*R*exp[-p]

{integral}pd[tex]\phi[/tex]dp.(p-2)*z*exp[-p] - with limits 0-2pi and 0-r

= -2pi*r^{2}*exp[-r]

so B(p,z)*2pi*p = 2pi*p*R*exp[-p] - 2pi*r^{2}*exp[-r]

= B(p,z) = p*R*exp[-p] - r^{2}/p*exp[-r]

is this answer right?

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

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Using stokes theorem to find magnetic field

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