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AC Components and Circuits
Inductance

Section 1-1 The Laws of Faraday and Lenz


Whenever a conductor is moving through a magnetic field, a voltage is induced in the conductor.

Faraday's Law

 

 

 

When a conductor moves through a field of magnetic flux, a voltage (emf) is induced in the conductor. This is basically how an electrical generator worksby moving a coil of wire through a strong magnetic field.

The faster the conductor moves, the greater the amount of emf induced in it.

The polarity of the induced emf depends on the direction of motion.

The motion between conductor and a magnetic field is relativethe field might be motionless  and the conductor is moving, or the conductor is motionless and the magnetic field is moving.

 

Definition

Faraday's Law

The amount of induced voltage is proportional to the rate of change of flux lines cutting the conductor.   

Vind = Df
Dt

where: 

Vind = the amount of induced voltage in volts (V) 
Df  = the rate of change of flux cutting the conductor in Webers/second (Wb/sec)
Dt

Faraday's Law for a Straight Wire

The amount of induced voltage is proportional to the rate of change of flux lines cutting the conductor.   

where: 

Vind = the amount of induced voltage in volts (V) 
= the rate of change of flux cutting the conductor in webers/second (Wb/sec)
The faster the rate of change of flux, the larger the amount of induced voltage. 

When there is no change in flux, there is no induced voltage.

 

 

Faraday's Law for a Coil of Wire 

The amount of induced voltage is proportional to the rate of change of flux and the number of turns of wire. 

 

Where: 

Vind = the amount of induced voltage in volts (V)
N = the number of turns of wire
= the rate of change of flux cutting the conductor in webers/second (Wb/sec)
Increasing the number of turns or the rate of change of flux increases the amount of induced voltage. 
 

 

 

 

 

Lenz's Law

 

 

 

lbldef.gif (1302 bytes)

Lenz's Law  

The voltage induced in a conductor will oppose the change in voltage that is causing the flux to change.

When an increasing voltage is applied to a conductor, the resulting increase in flux lines will induce a voltage that opposes the increase. 

When a decreasing voltage is applied to a conductor, the resulting decrease in flux lines will induce a voltage that opposes the decrease. 
 

 

 

 

 

 

 

 

 

 

 

 

David L. Heiserman, Editor

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All Rights Reserved

Revised: June 06, 2015