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MAXWELL’S EQUATIONS AND BOUNDARY CONDITIONS. Static field. Dynamic Field. Faraday’s Law. Electromotive force. Stationary Loop in a Time-varying Magnetic field. Lenz’s law. Faraday’s law, differential form. An example:. (a) The magnetic flux link of a single turn of the inductor.
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MAXWELL’S EQUATIONS AND BOUNDARY CONDITIONS Static field Dynamic Field
Electromotive force Stationary Loop in a Time-varying Magnetic field Lenz’s law
Faraday’s law, differential form An example: (a) The magnetic flux link of a single turn of the inductor. (b) The transformer emf,. (c) The polarity of the emf. (d) The induced current.
Example II Determine the voltage drops across the two resistors
The ideal Transformer properties: • = • I = 0 in the core. • The magnetic flux is confined within the core Questions: • I = ?, with applied voltage of V1and with RL • V2, and I2=?
Voltage transformer: Power relations: Why? Current transformer: Impedance transformer:
Another way to look at it: Next lecture: • The electromagnetic generator • Moving conductor in a time varying magnetic field
Moving conductor in a time-varying magnetic field Example: I
Displacement current • Ampere’s law in static electric field • Ampere’s law in time-varying electric field • proof of Ampere’s law: Displacement current density
Displacement current • Ampere’s law in time-varying electric field Example:
Boundary conditions for Electromagnetic Maxwell equations boundary conditions
Charge-Current continuity Relation charge current continuity equation steady state integral form Kirchhoff’s current law
Electromagnetic Potentials Electrostatics: Dynamic case:
Retard Potentials Electrostatics: Dynamic case:
Time-Harmonic Potentials if no free charge, trans-wave, why? • example find k?
n1 x n2 z