{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

lecture11 - Lecture 11 Faraday's Law and Electromagnetic...

Info icon This preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
1 ECE 303 – Fall 2007 – Farhan Rana – Cornell University Lecture 11 Faraday’s Law and Electromagnetic Induction and Electromagnetic Energy and Power Flow In this lecture you will learn: • More about Faraday’s Law and Electromagnetic Induction • The Non-uniqueness of Voltages in Magnetoquasistatics • Electromagnetic Energy and Power Flow • Electromagnetic Energy Stored in Capacitors and Inductors • Appendix (some proofs) ECE 303 – Fall 2007 – Farhan Rana – Cornell University Faraday’s Law Revisited a d H t a d B t s d E o r r r r r r . . . ∫∫ = ∫∫ = µ A closed contour B Faraday’s Law : The line integral of E- field over a closed contour is equal to –ve of the time rate of change of the magnetic flux that goes through any arbitrary surface that is bounded by the closed contour Important Note: In electroquasistatics the line integral of E-field over a closed contour was always zero In magnetoquasistatics this is NOT the case ( ) = = 0 . . s d s d E r r r φ
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
2 ECE 303 – Fall 2007 – Farhan Rana – Cornell University Electromagnetic Induction and Kirchoff’s Voltage Law Now consider a circuit through which the magnetic flux is changing with time (Kirchoff’s voltage law is violated) + + - - dt d a d B t s d E λ = ∫∫ = r r r r . . dt d V R I R I s d E λ = + = 2 1 . r r 1 R 2 R I ( ) ( ) dt d R R R R V I λ 2 1 2 1 1 + + = V + - ( ) t λ + + - - 1 R 2 R I V + - Kirchoff’s voltage law comes from the electroquasistatic approximation: 0 . = s d E r r 0 . 2 1 = + = V R I R I s d E r r ( ) 2 1 R R V I + = ECE 303 – Fall 2007 – Farhan Rana – Cornell University Lenz Law + + - - Suppose an induced current I is flowing through the wire: ( ) dt d R R I λ 2 1 1 + = 1 R 2 R I The induced current in the wire produces its own magnetic field Lenz Law is just an easy way to remember in which direction the induced current flows The law states that the induced current will flow in a direction such that its own magnetic field opposes the time variation of the magnetic field that produced it Example: Suppose the magnetic flux through the wire loop shown above was increasing with time (so that d λ / dt > 0). Lenz would tell us that the induced current would flow in the clockwise direction so that its own magnetic field would oppose the increasing magnetic flux through the loop In the equation above this fact comes out from the negative sign on the right hand side ( ) t λ
Image of page 2
3 ECE 303 – Fall 2007 – Farhan Rana – Cornell University Non-Uniqueness of Voltages in Magnetoquasistatics - I + + - - ( ) dt d R R I s d E λ = + = 2 1 . r r 1 R 2 R I 2 V 1 V Question: What is the voltages difference V 2 - V 1 ? One may be tempted to write ……. 1 1 2 2 2 1 V R I V V R I V = = 0 0 1 2 = = V V I ….. which cannot be correct since we know that: We have: What went wrong? Our usual concepts of circuit theory and potentials which are based on conservative E-fields are not valid when time varying magnetic fields are present ( ) dt d R R I λ 2 1 1 + = ( ) t λ
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern