Ampere's Law
Category : JEE Main & Advanced
Amperes law gives another method to calculate the magnetic field due to a given current distribution.
Line integral of the magnetic field \[\overrightarrow{B}\] around any closed curve is equal to \[{{\mu }_{0}}\] times the net current i threading through the area enclosed by the curve i.e.
\[\oint{\overrightarrow{B}\cdot \overrightarrow{dI}={{\mu }_{0}}\sum i}={{\mu }_{0}}({{i}_{1}}+{{i}_{3}}-{{i}_{2}})\]
Also using \[\overrightarrow{B}={{\mu }_{0}}\overrightarrow{H}\] (where \[\overrightarrow{H}=\] magnetising field)
\[\oint{{{\mu }_{0}}\overrightarrow{H}.\overrightarrow{dl}}={{\mu }_{0}}\Sigma i\]\[\Rightarrow \]\[\oint{\overrightarrow{H}.\overrightarrow{dl}=\sum i}\]
Total current crossing the above area is \[({{i}_{1}}+{{i}_{3}}-{{i}_{2}})\]. Any current outside the area is not included in net current. (Outward \[\to +ve\], Inward \[\to -ve\])
Biot-Savart's law v/s Ampere's law
| Biot-Savart's law | Ampere's law |
| this law is valid for all current distributions | This law is valid for symmetrical current distributions |
| This law is the differential form of \[\overrightarrow{B}\] or \[\overrightarrow{H}\] | Basically this law is the integral from of \[\overrightarrow{B}\] or \[\overrightarrow{H}\] |
| This law is based only on the principle of magnetism | This law is based on the principle of electromagnetism. |
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