Lect11VirtualWork - ECE 3030 Electromagnetic Fields and...

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1 ECE 3030 Electromagnetic Fields and Waves Fall 2009 Lecture 11 2009/9/21 Force, Energy, Power, and Work Energy Stored in Capacitors and Inductors Virtual Work 1 Rana and Swartz 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 11: Instructor: Dr. Wesley E. Swartz V + - + + + + + + + + - - - - - - - - ε B I I F F L Problem Assignments and Prelim 1 Demo 4 Problems: Problem 5.13 – Nano-dots, long, but straight forward. Problem 6.6 – N-turn coil with neat integration steps. Workshop 4 Problems: Problem 5.11 – Use of diverse spherical boundary conditions. Problem 6.5 – Applying Biot-Savart Law. No Homework 4 2 Rana and Swartz 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 11: No Homework 4. Prelim 1, Tuesday, September 29, 7:30pm: Covers Lectures 1-10, Text Chapters 1-6, Problem sets 1-4. Expect problems like in Demos, Workshops, and Homeworks, but with twists. The concepts of Problem 4.13 (Workshop 3) may be useful. Lorentz Force on Charges The force on a charge q in an E-field is: Example : consider two charges q 1 and q 2: E q F = q E 1 q 2 q d 2 1 ˆ n 3 Rana and Swartz 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 11: The force that q 1 exerts upon q 2 can be obtained by multiplying the E-field that q 1 produces at the location of q 2 by the charge q 2 : The force that q 2 exerts upon q 1 is just equal and opposite to what q 1 exerts upon q 2 (Newton’s third law): 2 1 2 o 1 2 1 2 2 1 n ˆ d 4 q q E q F = = π 1 2 2 2 1 2 1 2 2 1 1 2 ˆ 4 ˆ 4 = = n d q q n d q q F o o Potential Energy and Force The force on a charge q in an E-field is: The potential energy U of a charge in the E-field is: x x qE F = q E () x qE x q U x = = φ x x qE dx dU = Then note 4 Rana and Swartz 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 11: So the force on the charge can also be written as: This formula is much more general than it appears (see the slides down the road a bit …) dx dU F x = Electric force is the derivative of potential energy. Energy, Force, and Work in Electromagnetics Lets generalize the relationship between energy and force. Suppose one has a closed electromagnetic system with electromagnetic energy U . If the system does some mechanical work Fdx then its electromagnetic energy must decrease by the same amount: Fdx dU = 5 Rana and Swartz 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 11: Here “ F ” is some force that results in the change of some system length parameter by “ dx ”. Electromagnetic system or dx dU F = Force Between Charged Plates (1) Consider two charged plates carrying charges per unit area of σ and σ , respectively. area = A + + + + + + + + - - - - - - - - σ Need to find the total force on the right plate exerted by the left plate (which is also equal an opposite to the force on the left plate exerted by the right plate).
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Lect11VirtualWork - ECE 3030 Electromagnetic Fields and...

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