1. Lecture No.11 By. Sajid Hussain Qazi

2. Andre Ampere

3.  Coulomb’s Law (Superposition)  Gauss’s Law  This is used for high symmetry cases.

4.  Biot-Savart Law  Ampere’s Law ◦ Used for high symmetry cases.

5.  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

6. 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

7.  The current is uniformly distributed through the cross section of the wire

8.  Inside the wire, the current considered is inside the amperian circle Note the linear relationship of B with r

9.  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