1
28 magnetic induction
2
3
induced currents due to magnetic force qv x B
4
Faraday’s Law
• induced current due to qvB force can be determined in terms of magnetic flux
• flux definition same as before, with B replacing E
5
Faraday’s Law
• emf induced around closed loop:
6
Lenz’s Law
• The change in externally applied magnetic flux is opposed by the responsive magnetic flux change of a circuit.
• indicated by (-) sign in Faraday’s Law:
7
current direction determined from Lenz’s Law
8
9
Lenz’s Law: induced magnetic force opposes the motion
10
A metallic wire loop is in a uniform magnetic field.
Determine if there is a current induced in the loop when
•loop is stationary
•loop moves left or right
•loop moves upward out of the field region
11
A wire loop moves from a region with no magnetic field into a region with a uniform magnetic field pointing into the page. What is the direction of induced current in loop?
12
The loop is now entirely inside the B-field region
Apply Faraday’s Law to determine induced emf.
13
Example F.L.
• A loop of area 0.45 sq.m. is rotated 180 deg. in 0.15 seconds in uniform B = 1.2 tesla such that maximum flux change occurs. Calculate average emf induced.
14
flux through coil
• N = #turns of wire
• flux = NBAcos.
15
simple motor
16
Ex. The loop was inserted in 0.05s. The emf induced is
= NB(A)/t
= (80)(0.6)(ax/t)
= (80)(0.6)(0.2)(x/t)
= (80)(0.6)(0.2)(x/t)
= (80)(0.6)(0.2)(0.15/0.05)
= 28.8 volts
B = 0.6T
17
motional emf
18
motional emf: Eddy Currents produce resistive force.
19
The property of an electric circuit whereby an electromotive force is produced in the circuit by a change of current in the circuit itself. (McGraw-Hill Science Dict.)
L = (flux due to current)/current
self-inductance, L
dt
dIL
dt
LId
dt
d
)(
SI Unit: Henry, 1 H = 1 Wb/A
20
n= #turns/m
Example: n = 10,000 turns per meter, length 1.0m, and Area = 1.0m2.
L = (12.6x10-7)(10,000)2(1)(1) = 126H
L, solenoid
21
Magnetic Energydt
dIL
dt
dILIIP
dtdt
dIILPdt
“-” indicates power absorbed by inductor from battery. inductor gets a “+” of this.
Example: energy stored in a 126 henry coil with 1,000A
Um = ½ (126)(1,000)2 = 6.3x107 J = 63MJ.
22
SI Unit: joule per cubic meter, J/m3.
Ex. Calculate the energy density in a 5.0T field.
um = (5)2/(8x10-7) = 10 MJ/m3.
energy density
23
RL Circuits
24
0 IRdt
dIL
IRdt
dIL
L
dt
IR
dI
RdudI
RdIdu
IRu
/
integrate from t = 0 to t
integrate from I = 0 to I
25
RL Circuits
• “charging”
• “discharging”
• tau = L/R seconds
/1 teR
I
/teR
I
26
27
Inductors have resistive and inductive voltage drops
Ex. Current flow is increased through an inductor with L = 800mH and resistance r = 20 ohms at a rate of 30 amperes/second. The voltage when I = 2A is:
V = - (0.8)(30) – (2)(20) = -24 – 40 = -64 volts.
28
29
FL = qvd x B FR = qEperpendicularFup = qv x B