Lec7,8&9-EnergyPotential

Lec7,8&9-EnergyPotential - ECSE 351 Electromagnetic...

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ECSE 351 Electromagnetic Fields McGill University – ECE Dept. - Prof. Milica Popovi ć Lectures 7, 8 & 9: Energy and Potential ¾ Objective: concepts of field potential and energy contained in the field ¾ Why potential ? – A scalar field that offers simpler route to find electric field intensity than direct integration of Coulomb’s law ¾ How do we determine the energy contained in a region of space with electric field intensity?
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How did we define electric field intensity? If you want to move the test charge within the field, what do you need to “invest”? McGill – ECE – ECSE 351 Electromagnetic Fields – Prof. M. Popovic E JG A B
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Work = Force ×Distance If an external source wants to move charge Q by some small distance, it needs to contradict the electric field. Small (differential) work: dW Q E dL =− JJGJJG i McGill – ECE – ECSE 351 Electromagnetic Fields – Prof. M. Popovic E JG A B dL JJG
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Work = Force ×Distance If an external source wants to move charge Q by some small distance, it needs to contradict the electric field. Small (differential) work: McGill – ECE – ECSE 351 Electromagnetic Fields – Prof. M. Popovic dW Q E dL =− J JG J JG i “-” : We are opposing the field Force of the field Work is done along this short path
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Work required to move the charge a finite distance – integrate! McGill – ECE – ECSE 351 Electromagnetic Fields – Prof. M. Popovic dW Q E dL =− J JG J JG i “-” : We are opposing the field Force of the field Work is done along this short path finallocation initiallocation WQ E d L JJGJJG i
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Line integral McGill – ECE – ECSE 351 Electromagnetic Fields – Prof. M. Popovic final final initial initial L WQE d L QE d L =− ∫∫ J JG J JG i
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Differential length in coordinate systems: McGill – ECE – ECSE 351 Electromagnetic Fields – Prof. M. Popovic xyz z r dL dx a dy a dz a dL d a d a dz a dL dr a r d a r sin d a =++ =+ + + JJG JJ GJ J J G J J G ρφ θ φ ρρ θφ
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Gauss’s Law – application to determining the field of an infinite line charge ρ L totalinS 2 00 S d 2 zL z L DS D ()dd z = D( ) L Q L φ = == ρ φ = ρρ π = = ∫∫ JG JJG i v McGill – ECE – ECSE 351 Electromagnetic Fields – Prof. M. Popovic totalinS S d DS Q ψ= = J GJ J G i v If you take positive test-charge and move it circularly around the line charge along a closed path, work =? If you move it radially away from the line charge, work =?
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McGill – ECE – ECSE 351 Electromagnetic Fields – Prof. M. Popovic What happens when we integrate to obtain total work in each case?
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McGill – ECE – ECSE 351 Electromagnetic Fields – Prof. M. Popovic Potential = work done in moving a unit positive charge
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This note was uploaded on 01/10/2011 for the course ECSE 351 taught by Professor Davis during the Winter '08 term at McGill.

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Lec7,8&9-EnergyPotential - ECSE 351 Electromagnetic...

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