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

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

EEE340Lecture : 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)

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)

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.

EEE340Lecture : 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)