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EEE340Lecture 271 6-13: Magnetic Forces and Torques A moving charge q with velocity in a magnetic field of flux density experiences a force This equation is used to separate U 235 from U 238. 6-13.2: Forces on current carrying conductors The differential force exercised on a segment of current is Thus, the magnetic force on a loop C with current I is (6.183) (6.184) (6-4) (6-177)

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EEE340Lecture 272 When two circuits of I 1 and I 2 interact, the force on circuit 1 due to circuit 2 is Where is from the Biot-Savart law Hence (6.185a) (6.185b) (6.186)

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EEE340Lecture 273 Example 6-21: Determine the force. Per-unit length force Where hence (6.192) I1I1 I2I2 d x z y

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EEE340Lecture 274 Chapter 7: Time-Varying Fields and Maxwell’s Equation 7-2: Faraday’s Law In fact, (7.6) can be derived from (7.1). Show. Integrating (7.1), we have The LHS can be converted into line integral by Stoke’s theorem as The RHS (7.6) (7.1) (3.5) (7.4) (7.5)

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EEE340Lecture 275 7-2.2: Transformers Refer to EEE302 for details. 7-2.3: Moving conductor in static B-field 7-3: Maxwell’s Equations Displacement current

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EEE340Lecture 276 Example 7-5: An ac voltage source V(t)=V o sin t is connected to a parallel plate capacitor C 1. Determine the E-field, total current I. Solution: The conduction current in the wire The displacement

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EEE340Lecture 277 Maxwell’s Equations Differential formIntegral form (7.53a) (7.53b) (7.53c) (7.53d)

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EEE340Lecture 278 7-4: Potential functions Vector potential was introduced because Thus the Faraday’s law becomes i.e., Or (7.55) (7.56)

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EEE340Lecture 279 This is allowed because Hence (7.57)

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