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 U-shaped conductor with a movable rod, moving at velocity v. The area of the loop increases as it travels to the right

• This equation is valid if B, l, v are mutually perpendicular. This EMF is called motional EMF

dx

Blvdt

dxlB

dt

dAB

dt

dLawsFaradayFrom B

|:'

Induced EMF in a Moving Conductor in a Magnetic Field

• The magnetic force on the

electrons on the rod is

given by:

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:

BvqF

vBlq

W

q

UisEMFThelqvBdFW

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

• The power delivered to move the rod equal the power dissipated in the resistance of the rod.

R

vlBFext

22

R

lBv

RRIPP dispext

2222

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:

NBAwheretortNBA 00 sinsin

Electric Generators (AC)• The induced EMF is a sinusoidal voltage

• A typical AC Generator (Alternator):