physics
G
changing Bext ,
or changing A,
or changing θ
G
Bext =“external
magnetic field”
vector; unit=T
electromagnetic induction
Φ extB
G
G
= ∫ Bext • dA
G
For a uniform extB :
Φ extB = extB⊥ to surface ⋅ A
= extB|| to AG ⋅ A
= extB ⋅ A ⋅ cos θ
G
A is a vector whose
magnitude is the
surface’s area and whose
direction is normal to the
surface.
θ is the angle
G
G
between extB and A .
changing
Φ extB
“changing
magnetic flux
from the
external
magnetic
field”
scalar
units= V ⋅ s
Faraday’s law:
dΦ extB
Einduced = −
dt
extB
dΦ
dt
If Iind flows in positive
direction, then Eind>0;
if Iind flows in negative
direction, then Eind<0.
“induced
voltage”
“induced
emf”
|Einduced| =
Faraday’s law:
G
dΦ B
G
E
∫ ind •dr = − dt
G
Dir Eind is direction the
current would flow if it
existed.
Iinduced
Einduced
scalar
unit = V
= J/C
G
Eind
“induced
electric field”
“induced
current”
V=IR
Dir Iind is determined from
Lenz’s law:
1. Is Φ extB increasing or
decreasing?
2. Lenz’s law says that
G
dir Bind opposes the change
in Φ extB .
So, if Φ extB is increasing,
G
then dir Bind is opposite to
G
dir extB⊥surface ;
if Φ extB is decreasing, then
G
dir Bind is the same as
G
dir extB⊥surface .
3. Use the right-hand rule to
G
find dir Iind from dir Bind .
scalar
unit=A=C/s
vector
unit = N/C
extB
dBext dA
dΦ extB (t )
dΦ
d cos(θ )
. To find
you will need
First, get an expression, not a number, for Φ extB (t). Then, determine
,
, or
.
dt
dt
dt
dt
t
G
dB
dBext (t )
Changing Bext : If given ext , use it. If given an expression for Bext(t), find
.
dt
dt
dB
dBext ∆Bext
=
If given ∆Bext and ∆t with constant ext , find
.
dt
dt
∆t
dw
d cos(θ ) d cos( 2πft )
dA
Changing θ: θ = ωt = 2πft , so
Changing A: A = lw , so
=
= −2πf sin( 2πft ) .
=l
= lv .
dt
t
t
dt
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