Slide Presentations for ECE 329, Introduction to Electromagnetic Fields, to supplement “Elements of Engineering Electromagnetics, Sixth Edition” by Nannapaneni Narayana Rao Edward C. Jordan Professor of Electrical and Computer Engineering University of Illinois at Urbana-Champaign, Urbana, Illinois, USA Distinguished Amrita Professor of Engineering Amrita Vishwa Vidyapeetham, Coimbatore, Tamil Nadu, India

2.3 Faraday’s Law

Faraday’s Law

Voltage around C, also known as electromotive force (emf) around C (but not really a force), = Magnetic flux crossing S, = Time rate of decrease of magnetic flux crossing S,

Important Considerations (1) Right-hand screw (R.H.S.) Rule. The magnetic flux crossing the surface S is to be evaluated toward that side of S a right-hand screw advances as it is turned in the sense of C.

(2) Any surface S bounded by C. The surface S can be any surface bounded by C. For example: This means that, for a given C, the values of magnetic flux crossing all possible surfaces bounded by it is the same, or the magnetic flux bounded by C is unique.

(3) Imaginary contour C versus loop of wire. There is an emf induced around C in either case by the setting up of an electric field. A loop of wire will result in a current flowing in the wire. (4) Lenz’s Law. States that the sense of the induced emf is such that any current it produces, if the closed path were a loop of wire, tends to oppose the change in the magnetic flux that produces it.

Thus the magnetic flux produced by the Thus the magnetic flux produced by the induced current and that is bounded by C must be such that it opposes the change in the magnetic flux producing the induced emf. (5) N-turn coil. For an N-turn coil, the induced emf is N times that induced in one turn, since the surface bounded by one turn is bounded N times by the N-turn coil. Thus

where  is the magnetic flux linked by one turn

y y dec. wt y inc. wB0 wt –wB0 Lenz’s law is verified.

(b)

(c)

Motional emf concept conducting rails conducting bar

This can be interpreted as due to an electric field induced in the moving bar, as viewed by an observer moving with the bar, since

where is the magnetic force on a charge Q in the bar. Hence, the emf is known as motional emf.