Chapter 20  Induced voltages and inductance

20.1  Induced emf and Magnetic Flux 

•  Demo

< Induced emf >

•  An electric current can be produced by a changing magnetic field.  (Faraday’s observation)

< Magnetic Flux >

•  The magnetic flux is the amount of the magnetic field passing perpendicularly through an area multiplied by the area.

              F =  = B A cos

where B is the magnetic field, A area, and   the angle between the magnetic field and the normal to the area.

•  The unit of magnetic flux is Wb (Weber)

1 Wb = 1 T-m2 (tesla-meter-square).

[Note]  Fo = 2.0678 x 10-15 T-m2  : Flux quantum (fluxoid)

•  Figure 20.3

•  The magnetic flux is proportional to the number of field lines that passes through a surface.

20.2  Faraday’s Law of Induction

•  Whenever there is a change in flux through a loop of wire, an emf is induced in the loop.

 

  Faraday’s Law of Electromagnetic Induction 

The average emf E induced in a coil of N loops is

                   E = - N [(F - Fo)/(t – to)] = - N

where DF is the change in magnetic flux through one loop and Dt is the time interval during which the change occurs.  The term  is the average time rate of change of the flux that passes through one loop.

SI unit of induced emf : V (volt)

•  Examples

20.4 Lenz’s Law Revisited

•  Demo (Jumping ring)

  Lenz’s law 

The induced emf resulting from a changing magnetic flux has a polarity that leads to an induced current whose direction is such that the induced magnetic field opposes the original flux change.

  Reasoning Strategy 

1.   Determine whether the magnetic flux that penetrates a coil is increasing or decreasing.

2.   Find what the direction of the induced magnetic field must be so that it can oppose the change in flux by adding to or subtracting from the original field.

3.   Having found the direction of the induced magnetic field, use RHR-2 to determine the direction of the induced current.  Then the polarity of the induced emf can be assigned, because conventional current it directed out of the positive terminal, through the external circuit, and into the negative terminal.

•  Examples

22.2  Motional EMF

<The EMF Induced in a Moving Conductor>

•  When a conducting rode moves through a constant magnetic field, an emf is induced in a rod due to the magnetic force acting on a moving charge.

•  Figure 20.8 

•  The separated charges on the ends of the moving conductor give rise to an induced emf is called a motional emf.

•  The motional emf when , , and  are mutually perpendicular is given by

               = e = B  v

<Motional EMF and Magnetic Flux> 

•  Figure 20.9 

                   |e| =  

                      =

                      =

                      =  Bv

•  Examples

20.5  Generators (Reading Assignment)

20.6  Eddy Currents (Reading Assignment)

20.7  Self-Inductance

•  The effect in which a changing current in a circuit induces an emf in the same circuit is referred to as self-induction.

•  Figure 20.24 and 25

•  The emf due to self induction is

                   e = - L

where L is a proportionality constant called the inductance of the device.  The negative sigh indicates that a changing current induces an emf in opposition to that change.

•  The unit of inductance is H (Henry)

                   1 H = 1 V-s/A

•  Because of their self-inductance, coils are known as inductors.

                   L = N =

•  Examples

20.8  RL Circuits (Reading Assignment)

20.9  Energy Stored in a Magnetic Field

•  The energy stored in the magnetic field of an inductor carrying current I is

                   Energy = L I2