Download Induced EMF in a Moving Conductor

Unit 5 Day 2: Induced EMF in a Moving
Conductor
• Induced EMF in a Moving Conductor
in a Magnetic Field
• Force Required to Move a Moving
Conductor in a Uniform Magnetic
Field
• Electric Generators (AC)
Induced EMF in a Moving Conductor in
a Magnetic Field
• The B-Field is out of the paper and perpendicular to a Ushaped conductor with a movable rod, moving at velocity
v. The area of the loop increases as it travels to the right
d B
From Faraday ' s Law :|  
dt
dA
 B
dt
l  dx
 B
dt
dx 
 Blv
• This equation is valid if B, l, v are mutually
perpendicular. This EMF is called motional EMF
Induced EMF in a Moving Conductor in
a Magnetic Field
• The magnetic force on the
electrons on the rod is
given by: F  qv  B
where q is the charge on
the rod
• When the rod moves to the right with velocity v, electrons
in the rod also move with this speed & feel the force
• Another approach to calculating the EMF, is to determine
the work done to move a charge q, from one end of the
rod to the other: W  F  d  qvB  l The EMF is  U  W  vBl
q
q
The Force Required to Move a Conducting
Rod in a Uniform Magnetic Field
• To make the rod move to the right
an external force must be applied
in the direction of motion
2 2
Fext
B l v

R
• The power delivered to move the rod equal the power
dissipated in the resistance of the rod.
Pext  Pdisp
 v Bl
I R 
R
R
2
2
2 2
Electric Generators (AC)
• A mechanically turned armature, consisting of N-loops of
a coil wound on the armature
• As the armature is rotated, an EMF is induced in the
rotating coil, which alternates as the magnetic flux
through the loop reverses. The induced EMF is:
  NBA sin t  or 0 sin t  where 0  NBA
Electric Generators (AC)
• The induced EMF is a sinusoidal voltage
• A typical AC Generator (Alternator):