M7 - Phy sics 7B WS M7 (rev. 2.1) Page 1 M-7. Displacement...

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Physics 7B WS M7 (rev. 2.1) Page 1 M-7. Displacement Current and Maxwell’s Equations Part 1: Displacement Current I D = " 0 d dt r E # d r A surface $$ Questions for discussion (Part 1) 1 . In the version of Ampere’s Law that we have been working with up to now, we had to find the current enclosed by a loop. How did you determine whether a current was ‘enclosed’ or not? Try to relate the calculation of ‘enclosed current’ to the calculation of a flux through a surface. 2. In Faraday’s Law, why did it not matter which surface you are calculating the flux through, as long as the surface is bounded by a given closed loop? 3. Consider a closed surface. For steady state configurations (which is what we were working with in magnetostatics), what is the net amount of current piercing the surface? (Consider current entering the surface to be negative and current leaving the surface to be positive.) 4. Why do we need to add another term to Ampere’s Law to make it consistent? 5. How is the net displacement current entering a closed surface related to the net actual current entering that same surface?
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Physics 7B WS M7 (rev. 2.1) Page 2 6. What are the units of electric flux? Show that the displacement current indeed has the units of a current. 7. A single point charge q is located on the z-axis a little bit above the xy-plane. If the charge moves upwards with speed v, how much displacement current flows through the xy plane? 8. Two circular plates have equal but opposite charges q that vary with time. a) If the plates are charging up , draw the magnetic field created between the plates as a result of the changing electric field. (Think of the changing electric field as a current flowing in the direction of the change.) b) Draw the magnetic field created between the plates when the plates are charging down.
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Physics 7B WS M7 (rev. 2.1) Page 3 Problems (Part 1) 1. Consider an infinitely long current-carrying wire connected to a circular place capacitor of radius R and separation d, with R>>d. Ignore all fringing effects in this problem and assume that the charge is uniformly distributed over the capacitor plate. a) At a certain instant in time, the charge on the capacitor is q(t) and the current in the wire is i(t). Find the electric and magnetic fields everywhere, ignoring the effects of Faraday’s Law and the displacement current. b) At the instant in time considered above, what is the rate of change of the electric field between the capacitor plates? c) Consider an Amperean loop of radius r<R between the capacitor plates. What is the displacement current enclosed by this loop? d) Find the displacement current density everywhere between the plates, j D (r,t). e)
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This note was uploaded on 11/19/2010 for the course LECTURE 1 taught by Professor Yildiz during the Fall '10 term at Berkeley.

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M7 - Phy sics 7B WS M7 (rev. 2.1) Page 1 M-7. Displacement...

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