Lecture No.11 By. Sajid Hussain Qazi
Andre Ampere
Coulomb’s Law (Superposition) Gauss’s Law This is used for high symmetry cases.
Biot-Savart Law Ampere’s Law ◦ Used for high symmetry cases.
For small length elements ds on a closed path (not necessarily circular) I is enclosed current passing through any surface bounded by the closed path. Use where there is high symmetry ds I B
Sign Convention for the Current in Ampere’s Law r The current I passing through a loop is positive if the direction of B from the right hand rule is the same as the direction of the integration (ds). r positive I I B ds I B negative I
The current is uniformly distributed through the cross section of the wire
Inside the wire, the current considered is inside the amperian circle Note the linear relationship of B with r
The field is proportional to r inside the wire The field varies as 1/r outside the wire Both equations are equal at r = R