Advanced General Physics 323/324

Electricity and Magnetism Unit E4: Electromagnetic Induction

Prerequisite: E3

Overview:

In this unit we consider the effects of changing magnetic fields. First we discuss the electric field, called the induced electromotive force (EMF), produced by a changing magnetic field. This is the basis for many useful devices such as inductances and transformers, and will enable us to calculate the energy stored in a magnetic field.

Section I: Induced EMF

Read:

E. M. Purcell, Electricity and Magnetism, Berkeley Physics Course, Vol. 2, 2nd Ed. , Chapt. 7 - Electromagnetic Induction, Sec. 7.1-7.10, ;Chapt. 2, Sec. 2.13-2.16

Understand:

  • Faraday's law and induced EMF.
  • The minus sign in the equations and Lenz's law.
  • The force on a current element placed in a magnetic field (magnitude and direction).
  • How the induced electric field is not like an electrostatic field; the circulation of E.
  • Problems:

    Purcell 7.1,7.2,7.3,7.14
  • An electric field is uniform in x and points in the x direction but is proportional to y: E = C y i , where i is a unit vector in the +x direction and C is a constant. Can this field exist in the absence of a magnetic field? Can it be an electrostatic field? What can you say about the electric flux through a closed surface in this region?

    Section II: Inductance

    Read:

    E. M. Purcell, Electricity and Magnetism, Berkeley Physics Course, Vol. 2, 2nd Ed. , Chapt. 7 - Electromagnetic Induction, Sec. 7.8, 7.7 (to bottom of p.279 , 7.8,7.10.

    Understand::

  • Energy of a current loop in a magnetic field.
  • Mutual inductance, flux linkage.
  • Self-inductance and how to calculate it.
  • Energy per volume stored in a magnetic field: u = B2/(8π).
  • Problems: Purcell 7.7,7.21,7.23


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