Displacement Current May 7, 2007

+ Moving circuit but constant ,
direction of integration is opposite to
Example 4.17: Induced voltage from a moving circuit (time varying area)

+ Displacement current (Sect. 6.3) -- , e.g. ac current in capacitor

+ Complete Maxwell's eqns: obtain the phasor form by substituting with etc




Note: displacement current increases with freq.

+ Boundary: ; ; ;
Note: is pointing from medium 2 to medium 1; time varying field inside a perfect conductor
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HW #24 (no late homework) 5/9/07
1. Find the mutual inductance between two coplanar rectangular loops with parallel sides as shown in the following diagram. Assume that . (modified Problem 5.17 on page 226).
2. Consider the toroidal core in problem 2b of HW 22. a) Find an expression for the stored magnetic energy. b) Determine self-inductance from magnetic energy. (Note: check exercise 5.9 on page 213 and example 4.15 on the web)
3. A stationary rectangular conducting loop of width w and height h is situated near a very long wire carrying current as in the following diagram. Assume and the self-inductance of the rectangular loop to be L. Find the induced current in the loop. (modified Problem 6.3 on page 268)
4. A conducting bar can slide freely over two conducting rails as shown in Fig. 6-4 (page 237) with h=6cm. Calculate the current flowing in R
a) If the bar is stationed at x=8cm and ; b) if the bar slides at a velocity m/s and ; c) if the bar slides at a velocity m/s and .


Extra-credit
5. Problem 6.4 (page 268) (Hint: show that the open loop induced voltage is ).
6. Consider Fig. 6-11 (page 269) except that the loop has 10 turns, let connected to two terminal of the 10-turns-loop and the loop is rotating at an angular frequency (rad/s). Assume self-inductance of the loop is negligible.
a) If , find the induced current.
b) If , find the induced current.