- #1
AdkinsJr
- 150
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I'd rather not post the exact problem since it's homework, I don't think my instructor in E&M would want me posting full problems but I will just ask relevant conceptual question...
Let's say we I have a long cylinder with time-defendant surface current density [tex]\vec K(t)=K_of(t)[/tex]. So if I want to find the B-field, can I still use ampere's law? My idea was to find current from the definition of surface current density,
[tex]\vec K(t) =\frac{dI}{dl_{\perp}}=K_of(t) [/tex]
EDIT: the direction of K is in the "phi" direction in cylindrical coordinate, the field is therefore oriented along the positive z-axis...
So now I have [tex]I(t)=\int K_of(t) dl_{\perp}=K_of(t)\int dl_{\perp}[/tex]
I'm kind of skeptical about find the E-field everywhere by applying ampere's law to find the B-field, then finding the flux, then using faraday's law to find the field. There is a problem in my text in which a "quasistatic approximation" is used to find the B-field given a time-varying current, where basically they just treated it as you would in magnetostatics. So do I need to assess if f(t) is slow enough for the approximation or can enclosed current be a function of time?
[tex]\int \vec B \cdot \vec dl = \mu_oI_{enc}(t)[/tex]
It kind of makes sense since I could just claim it is a time-dependant b-field when I apply ampere's law.
To summerize, basically I'm trying to use K to find I, then use I to find B, then use B to find flux, then use flux to find E... can this be done?
Let's say we I have a long cylinder with time-defendant surface current density [tex]\vec K(t)=K_of(t)[/tex]. So if I want to find the B-field, can I still use ampere's law? My idea was to find current from the definition of surface current density,
[tex]\vec K(t) =\frac{dI}{dl_{\perp}}=K_of(t) [/tex]
EDIT: the direction of K is in the "phi" direction in cylindrical coordinate, the field is therefore oriented along the positive z-axis...
So now I have [tex]I(t)=\int K_of(t) dl_{\perp}=K_of(t)\int dl_{\perp}[/tex]
I'm kind of skeptical about find the E-field everywhere by applying ampere's law to find the B-field, then finding the flux, then using faraday's law to find the field. There is a problem in my text in which a "quasistatic approximation" is used to find the B-field given a time-varying current, where basically they just treated it as you would in magnetostatics. So do I need to assess if f(t) is slow enough for the approximation or can enclosed current be a function of time?
[tex]\int \vec B \cdot \vec dl = \mu_oI_{enc}(t)[/tex]
It kind of makes sense since I could just claim it is a time-dependant b-field when I apply ampere's law.
To summerize, basically I'm trying to use K to find I, then use I to find B, then use B to find flux, then use flux to find E... can this be done?
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