1 28 magnetic induction. 2 3 induced currents due to magnetic force qv x B.
-
Upload
hollie-dawson -
Category
Documents
-
view
213 -
download
0
Transcript of 1 28 magnetic induction. 2 3 induced currents due to magnetic force qv x B.
![Page 1: 1 28 magnetic induction. 2 3 induced currents due to magnetic force qv x B.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e7e5503460f94b818b0/html5/thumbnails/1.jpg)
1
28 magnetic induction
![Page 2: 1 28 magnetic induction. 2 3 induced currents due to magnetic force qv x B.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e7e5503460f94b818b0/html5/thumbnails/2.jpg)
2
![Page 3: 1 28 magnetic induction. 2 3 induced currents due to magnetic force qv x B.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e7e5503460f94b818b0/html5/thumbnails/3.jpg)
3
induced currents due to magnetic force qv x B
![Page 4: 1 28 magnetic induction. 2 3 induced currents due to magnetic force qv x B.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e7e5503460f94b818b0/html5/thumbnails/4.jpg)
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
![Page 5: 1 28 magnetic induction. 2 3 induced currents due to magnetic force qv x B.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e7e5503460f94b818b0/html5/thumbnails/5.jpg)
5
Faraday’s Law
• emf induced around closed loop:
![Page 6: 1 28 magnetic induction. 2 3 induced currents due to magnetic force qv x B.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e7e5503460f94b818b0/html5/thumbnails/6.jpg)
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:
![Page 7: 1 28 magnetic induction. 2 3 induced currents due to magnetic force qv x B.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e7e5503460f94b818b0/html5/thumbnails/7.jpg)
7
current direction determined from Lenz’s Law
![Page 8: 1 28 magnetic induction. 2 3 induced currents due to magnetic force qv x B.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e7e5503460f94b818b0/html5/thumbnails/8.jpg)
8
![Page 9: 1 28 magnetic induction. 2 3 induced currents due to magnetic force qv x B.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e7e5503460f94b818b0/html5/thumbnails/9.jpg)
9
Lenz’s Law: induced magnetic force opposes the motion
![Page 10: 1 28 magnetic induction. 2 3 induced currents due to magnetic force qv x B.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e7e5503460f94b818b0/html5/thumbnails/10.jpg)
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
![Page 11: 1 28 magnetic induction. 2 3 induced currents due to magnetic force qv x B.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e7e5503460f94b818b0/html5/thumbnails/11.jpg)
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?
![Page 12: 1 28 magnetic induction. 2 3 induced currents due to magnetic force qv x B.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e7e5503460f94b818b0/html5/thumbnails/12.jpg)
12
The loop is now entirely inside the B-field region
Apply Faraday’s Law to determine induced emf.
![Page 13: 1 28 magnetic induction. 2 3 induced currents due to magnetic force qv x B.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e7e5503460f94b818b0/html5/thumbnails/13.jpg)
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.
![Page 14: 1 28 magnetic induction. 2 3 induced currents due to magnetic force qv x B.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e7e5503460f94b818b0/html5/thumbnails/14.jpg)
14
flux through coil
• N = #turns of wire
• flux = NBAcos.
![Page 15: 1 28 magnetic induction. 2 3 induced currents due to magnetic force qv x B.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e7e5503460f94b818b0/html5/thumbnails/15.jpg)
15
simple motor
![Page 16: 1 28 magnetic induction. 2 3 induced currents due to magnetic force qv x B.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e7e5503460f94b818b0/html5/thumbnails/16.jpg)
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
![Page 17: 1 28 magnetic induction. 2 3 induced currents due to magnetic force qv x B.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e7e5503460f94b818b0/html5/thumbnails/17.jpg)
17
motional emf
![Page 18: 1 28 magnetic induction. 2 3 induced currents due to magnetic force qv x B.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e7e5503460f94b818b0/html5/thumbnails/18.jpg)
18
motional emf: Eddy Currents produce resistive force.
![Page 19: 1 28 magnetic induction. 2 3 induced currents due to magnetic force qv x B.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e7e5503460f94b818b0/html5/thumbnails/19.jpg)
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
![Page 20: 1 28 magnetic induction. 2 3 induced currents due to magnetic force qv x B.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e7e5503460f94b818b0/html5/thumbnails/20.jpg)
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
![Page 21: 1 28 magnetic induction. 2 3 induced currents due to magnetic force qv x B.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e7e5503460f94b818b0/html5/thumbnails/21.jpg)
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.
![Page 22: 1 28 magnetic induction. 2 3 induced currents due to magnetic force qv x B.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e7e5503460f94b818b0/html5/thumbnails/22.jpg)
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
![Page 23: 1 28 magnetic induction. 2 3 induced currents due to magnetic force qv x B.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e7e5503460f94b818b0/html5/thumbnails/23.jpg)
23
RL Circuits
![Page 24: 1 28 magnetic induction. 2 3 induced currents due to magnetic force qv x B.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e7e5503460f94b818b0/html5/thumbnails/24.jpg)
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
![Page 25: 1 28 magnetic induction. 2 3 induced currents due to magnetic force qv x B.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e7e5503460f94b818b0/html5/thumbnails/25.jpg)
25
RL Circuits
• “charging”
• “discharging”
• tau = L/R seconds
/1 teR
I
/teR
I
![Page 26: 1 28 magnetic induction. 2 3 induced currents due to magnetic force qv x B.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e7e5503460f94b818b0/html5/thumbnails/26.jpg)
26
![Page 27: 1 28 magnetic induction. 2 3 induced currents due to magnetic force qv x B.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e7e5503460f94b818b0/html5/thumbnails/27.jpg)
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.
![Page 28: 1 28 magnetic induction. 2 3 induced currents due to magnetic force qv x B.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e7e5503460f94b818b0/html5/thumbnails/28.jpg)
28
![Page 29: 1 28 magnetic induction. 2 3 induced currents due to magnetic force qv x B.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e7e5503460f94b818b0/html5/thumbnails/29.jpg)
29
FL = qvd x B FR = qEperpendicularFup = qv x B