Physics 212
Lecture 17
Faraday’s Law
dB
E

dl



dt
Physics 212 Lecture 17, Slide 1
Main Point 1
First, we introduced the concept of the magnetic flux and found that the motional
emfs produced in the three examples from the last prelecture could all be written
simply as the time rate of change of the magnetic flux through the circuit.
Physics 212 Lecture 17, Slide 2
Main Point 2
Second, we introduced Faraday’s Law, which states that whenever magnetic flux
changes in time, not just in the case of a moving conductor, an emf will be produced.
In particular, this induced emf will just be equal to minus the time rate of change
of the magnetic flux.
Physics 212 Lecture 17, Slide 3
Main Point 3
Finally, we observed that this induced emf is determined by integrating the electric
field around the loop, so that Faraday’s law can be written more generally only in
terms of the electric and magnetic fields. A changing magnetic flux creates an
electric field. Faraday’s law represents the first important step in establishing the
deep connections between electric and magnetic fields which ultimately will explain
the existence of electromagnetic waves and the identification of light as an
Physics 212 Lecture 17, Slide 4
electromagnetic phenomenon.
Faraday’s Law
dB
emf   E  dl  
dt
 B   B  dA
Looks scary but it’s not – its amazing and beautiful !
A changing magnetic flux produces an electric field.
Electricity and magnetism are on intimate terms
Physics 212 Lecture 17, Slide 5
Faraday’s Law:
 
d B
emf   E  d   
dt
where
 
 B   B  dA
In Practical Words:
1) When the flux B through a loop changes, an emf is induced in the
loop.
B
A
Show Projection
Think of B as the number of field lines passing through the surface
There are many ways to change this…
Physics 212 Lecture 17, Slide 6
Physics 212 Lecture 17, Slide 7
Faraday’s Law
dB
emf   E  dl  
dt
 B   B  dA
In Words:
1) When the flux B through a loop changes, an emf is induced in the loop.
2) The emf will make a current flow if it can (like a battery).
3) The current that flows induces a new magnetic field.
4) The new magnetic field opposes the change in the original magnetic
field.
B
dB/dt
Physics 212 Lecture 17, Slide 8
The Ways Flux Can Change
Change Area
Change magnetic field
Change orientation
ALL THESE CHANGES CAN BE UNDERSTOOD FROM MOTIONAL EMF
WHAT’S NEW WITH FARADAY?
Flux can change WITHOUT moving any conductor !!
e.g., change current that produces magnetic field
Physics 212 Lecture 17, Slide 9
Faraday’s Law
dB
emf   E  dl  
dt
 B   B  dA
Executive Summary:
emf→current→field a) induced only when flux is changing
b) opposes the change
Physics 212 Lecture 17, Slide 10
Physics 212 Lecture 17, Slide 11
Checkpoint 1a
A copper loop is placed in a uniform magnetic field as shown. You are looking from the right.
Suppose the loop is moving to the right. The current induced in the loop is:
A. zero
B. clockwise
C. counterclockwise
Physics 212 Lecture 17, Slide 12
Checkpoint 1b
A copper loop is placed in a uniform magnetic field as shown. You are looking from the right.
Now suppose the that loop is stationary and thatCheckpoint
the magnetic field
1b is
decreasing in time. The current induced in the loop is:
A. zero
B. clockwise
C. counterclockwise
Physics 212 Lecture 17, Slide 13
Checkpoint 1c
Now suppose that the loop is spun around a vertical axis as shown, and that it makes one
complete revolution every second.
The current induced in the loop:
A. Is zero
B. Changes direction once per second
C. Changes direction twice per second
Physics 212 Lecture 17, Slide 14
Checkpoint 2
A horizontal copper ring is dropped from rest directly above the north pole of a permanent magnet
O
X
B
B
(copper is not
ferromagnetic)
Will the acceleration a of the falling ring in the presence of the magnet
be any different than it would have been under the influence of just
gravity (i.e. g)?
A. a > g
B. a = g
C. a < g
Physics 212 Lecture 17, Slide 15
Physics 212 Lecture 17, Slide 16
Calculation
A rectangular loop (height = a, length = b,
resistance = R, mass = m) coasts with a constant
velocity v0 in + x direction as shown. At t =0, the
loop enters a region of constant magnetic field B
directed in the –z direction.
y
a
v0
B
b x x x x x x x
x x x x x x x
x x x x x x x
x x x x x x x
x
What is the direction and the magnitude of the
force on the loop when half of it is in the field?
Conceptual Analysis
Strategic Analysis
Physics 212 Lecture 17, Slide 17
Physics 212 Lecture 17, Slide 18
Physics 212 Lecture 17, Slide 19
Physics 212 Lecture 17, Slide 20