Download Electromagnetic Induction

A.S. 12.1.1 – 12.1.6 due Friday, 12/19/14
Things to think about…

 What happens to electrons as they move through a
magnetic field?
 What would happen if there were a LOT of
electrons…like in a wire…
What happens…

 Electrons experience a force when moving through a
magnetic field
 If the electrons are in a wire, they all experience a
force and will move in the direction of the force
 Result: A net shift in charge so that one side of the
wire is more negative than the other
 End result: There is an electric field created in the
wire due to the separation of charges:
∆𝑉 𝑉
𝐸=
=
∆𝑥 𝐿
Induced (motional) emf

 The electrons (charge = e) will continue to move to
one end of the wire UNTIL…
 The force of electrostatic repulsion balances the force
from the magnetic field:
𝑒𝐸 = 𝑒𝑣𝐵
𝐸 = 𝑣𝐵
𝑉
= 𝑣𝐵
𝐿
𝑽 = 𝑳𝒗𝑩
Electromagnetic
Induction

Known: An electric current produces a
magnetic field
Known: A wire moving through
(perpendicular to) a magnetic field will
develop a potential difference across its ends
(Induced emf)
More difficult? Producing a current…
Observations

What happens to the current when:
 North end moved into the loop?
 North end moved out of the loop?
 South end moved into the loop?
 South end moved out of the loop?
 North end held above the plane of the loop?
 Magnet held inside the loop?
 Magnet moved in/out of the loop at a different speed
than before?
Variables that affect current:
As these increase, so will the current:

 The relative speed of the magnet with respect to the
loop/coil
 Strength of the magnetic field
 Number of turns in the coil
 Area of the loop
ALSO:
 Angle of the magnetic field relative to the plane of the
loop.
 At an angle 90° (field perpendicular to the plane of the
loop), the current will be the maximum possible for the
conditions
Michael Faraday

 British Physicist and Chemist—born 1791, died 1867
 Self-taught…discovered many concepts, had difficulties
with some of the math 
 Discovered Electromagnetic Induction in 1831
 (also devised the laws relating to electrolysis and the
deposition of ions onto metals through the use of electricity)
 Found the connecting link between each of the
observations we just made…
 The relevant law that bears his name (Faraday’s Law)
relates to electromagnetism
Magnetic Flux

 The strength of the magnetic field crossing the
plane of a loop of area, A
Φ = 𝐵 ∙ 𝐴𝑐𝑜𝑠𝜃
 B = magnetic field strength
 A = area of the loop
 q = angle between the magnetic field direction
and the normal to the plane of the loop
Magnetic Flux

 Units of flux = Weber (Wb)
 Conceptual visualization: flux is the number of
magnetic field lines that are passing through the
plane of the loop
 Increase the flux by:
 Increasing the area of the loop
 Increasing the strength of the field (more field lines…)
 Making the loop and field lines more perpendicular
Magnetic Flux Linkage

 Same as magnetic flux…but specifically when there
is more than 1 loop in a coil.
Φ = 𝑁 ∙ 𝐵 ∙ 𝐴𝑐𝑜𝑠𝜃
 N = number of loops in the coil
Sample Problem

 A loop of area 2.00 cm2 is in a constant magnetic field
of 0.100 T. What is the magnetic flux through the
loop in each of the following situations:
 When the loop is perpendicular to the field
 When the loop is parallel to the field
 When the normal to the loop and the field have an
angle of 60.0° between them?
Faraday’s Law

 The induced emf is equal to the (negative value for)
rate of change of magnetic flux:
∆Φ
𝜀 = −𝑁
∆𝑡
 The induced emf, therefore, can cause a current in a
conducting wire…but this will ONLY happen when
there is a changing magnetic flux!
Sample Problem

 The magnetic field through a single loop of area
0.250 m2 is changing at a rate of 4.25 T·s-1. What is
the induced emf in the loop?
