Applications of Ampere law:-
- Infinite straight current carrying wire:-
In this the current is longitudinal (source is longitudinal) but the field produced is circumferential. The magnetic field is tangential to every point of the observed path.
- M.F of cylindrical current carrying wire:-
A cylindrical wire having radius ‘R’, carrying an uniform current density\(overrightarrow{J}\) . Once again the current here is longitudinal.
The magnetic field will be circumferential. We can choose a circular path as the integration path to calculate the magnetic field anywhere.
Inside:- \(oint{overrightarrow{B}}cdot overrightarrow{dell }={{mu }_{o}}{{I}_{net}}\) \(Btimes 2cancel{pi }cancel{r}=mu o(Jcancel{pi }{{r}^{cancel{2}}})\) \(B=frac{{{mu }_{o}}Jr}{2},,,,,overrightarrow{B}left( rle R right)=frac{{{mu }_{o}}(overrightarrow{J}times overrightarrow{r})}{2}\)
Outside:- \(B=2cancel{pi }r={{mu }_{o}}J(cancel{pi }{{R}^{2}})\) \(B=frac{{{mu }_{o}}J{{R}^{2}}}{2r},,,,,overrightarrow{B}(rge R)=frac{{{mu }_{o}}{{R}^{2}}}{2r}(overrightarrow{J}times hat{r})\)
For outside points, the M.F is similar to the field attained in case of a st. current carrying wire. That means, for outside points it is behaving as if the entire current is passing through the axis.
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