1. EEE340Lecture 211 Example 6-2: A toroidal coil of N turns, carrying a current I. Find Solution Apply Ampere’s circuital law. Hence (6.13) b a

2. EEE340Lecture 212 Example 6-3: Long solenoid with n turns per unit length which carries a current I. Determine inside. Solution From symmetry, the field inside must be parallel to the axis. From Ampere’s law, i.e. Note: there is no B fields outside the solenoid (6.14) B L

3. EEE340Lecture 213 6-3: Vector Magnetic Potential The vector magnetic potential Which is a dual of the electric scalar potential Where The magnetic flux density Eq (6.15) is valid because (6.23) (3.61) (6.15)

4. EEE340Lecture 214 Note that the correspondences between fields and circuits are: But and I are governed by Ampere’s circuital law in 90 o. According to (6.23), aligns with is 90 o with Therefore and I are 90 o apart. The magnetic flux  through a given area S, bounded by contour C is (6.24, 6.25)

5. EEE340Lecture 215 Project The discretized Laplace equation has a simple physical meaning that the potential at a node is the average is its (4) neighbors (2D). The derivation is in the project handout.

6. EEE340Lecture 216 6-4: Biot-Savart Law The differential magnetic due to a differential segment of current where For a closed path C’ of current I In contrast, the electric field (6.33) (6.32)