Electromagnetic Induction notes for DU students
Electromagnetic Induction notes for DU students

ELECTROMAGNETIC INDUCTION (Chapter 29)

INDUCTANCE (Chapter 30) below

 

KEY TERMS: induced current, induced emf, Faraday's law of induction, Lenz's law, motional emf, induced electric field, Maxwell's equations.

 

 
Fig. 29.1 Induction of a current in a coil of wire
  
 

Whenever there is a change in the number of magnetic field lines passing through a loop of wire a voltage (or emf) is generated (or induced) in the loop of wire. This is how an electric generator works. The phenomenon is known as electromagnetic induction and is explained by 
Faraday's law of induction:
e = -- dF / dt

where F is the magnetic flux given by the closed integral of the dot product B 0 dA.

 

 

 

 

 

 

According to Faraday's law,
if there is no change (with time) 
in the number of lines of B field, 
or magnetic flux, 
through a closed loop(s) 
there will be no induced, 
or generated, 
voltage set up in the loop(s).
Fig. 29.2 Coil in a uniform constant magnetic field
  

 

 

 
Fig. 29.3 Magnetic flux (F)
  

 

 

 

 

According to Faraday's law, as the 
strength of a magnetic field (B) passing through a loop of wire increases, there 
will be an increase in the number of magnetic field lines, and therefore an induced voltage, or emf, 
set up in the wire loop.

If the strength decreases there will also 
be an induced emf set up in the loop but with the opposite polarity.

Lenz's law indicates the polarity
of the induced emf.
Fig. 29.5 Coil in an increasing magnetic field
  

 

 

 

 
Fig. 29.6 Changing magnetic flux induces current (recall I = V / R)
  

 

 

 

 
Fig. 29.8 Alternator (AC generator)
  

In an AC electric generator, or alternator, the flux through the loops of wire (wound on the armature) changes, and therefore according to Faraday's law there will be an emf induced in the loops of wire.
This induced emf causes a current to flow in the loops.

 

 
Fig. 29.10 DC generator
  

In a DC generator the direction of the induced current in the loops must be changed every one-half
turn of the generator shaft. This is done with split rings on the rotating armature contacting the 
stationary "brushes" which are in turn connected to the wires coming out of the generator.

 

 

 

There is another way to see how a current is set up in the loop. 
The electric force equation F = q v x B and the right hand rule indicate there is a force on the charges (electrons) in the purple bar that is moving with velocity v.

 

Fig. 29.11Slidewire generator
Because the magnetic flux (F) through the loop is changing (increasing) there is an emf induced in the loop in accordance with Faraday's law. 

  

 

 

 
Fig. 29.12 Induced current (I) causes a force F = I L x B to be exerted on the bar. 
This force is in the direction opposite to the velocity v.
  

 

 

 

 
Fig. 29.13 Lenz's law describes the tendency of nature to resist any 
change in magnetic flux passing through a loop of wire. 
Changes in flux can be canceled by inducing a magnetic field in the appropriate direction.
  

 

 

 

 
Fig. 29.14 Induced currents caused by changes in magnetic flux
  

 

 

 

 
Fig. 29.15 (a) Induced emf in rod, (b) induced current in wire loop
  

 

 

 

 
Fig. 29.17 Solenoid with changing current. 
The galvanometer G will record the presence of an induced emf in the loop of wire 
caused by the change in flux passing through the loop.
  

 

 

 

 
Fig. 29.19 Eddy currents
  

 

 

 

 
Fig. 29.20 Metal detector
  

 

 

 

Maxwell's Equations (section 29.7) will be covered later in Chapter 32 "Electromagnetic Waves." 

Maxwell's four equations 

1. Gauss's Law for electric fields 
2. Gauss's Law formagnetic fields, 
3. Faraday's Law, and 
4. Ampere's Law as modified by Maxwell 

predict the existence of electromagnetic waves capable of propagating through empty space at the speed of light, which is an electromagnetic wave.
  

 

 

 

  

 

 
Fig. 29.31 Lenz's law
  

 

 

 

 
Fig. 29.33 Lenz's law (Exercise 29.17)
  

 

 

 

 
Fig. 29.34 Lenz's law (Exercise 29.18)
  

 

 

 

 
Fig. 29.37 Lenz's law (Exercise 29.21)

By Ashish Kumar Yogi
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