the magnetic field the force on a charge q moving with a velocity the magnitude of the force
Post on 20-Dec-2015
225 views
TRANSCRIPT
![Page 1: The Magnetic Field The force on a charge q moving with a velocity The magnitude of the force](https://reader035.vdocument.in/reader035/viewer/2022062216/56649d485503460f94a22e8f/html5/thumbnails/1.jpg)
![Page 2: The Magnetic Field The force on a charge q moving with a velocity The magnitude of the force](https://reader035.vdocument.in/reader035/viewer/2022062216/56649d485503460f94a22e8f/html5/thumbnails/2.jpg)
The Magnetic Field
![Page 3: The Magnetic Field The force on a charge q moving with a velocity The magnitude of the force](https://reader035.vdocument.in/reader035/viewer/2022062216/56649d485503460f94a22e8f/html5/thumbnails/3.jpg)
![Page 4: The Magnetic Field The force on a charge q moving with a velocity The magnitude of the force](https://reader035.vdocument.in/reader035/viewer/2022062216/56649d485503460f94a22e8f/html5/thumbnails/4.jpg)
![Page 5: The Magnetic Field The force on a charge q moving with a velocity The magnitude of the force](https://reader035.vdocument.in/reader035/viewer/2022062216/56649d485503460f94a22e8f/html5/thumbnails/5.jpg)
The force on a charge q moving with a velocity F
v
)( BvEqF
The magnitude of the force
sinqvBF
sec)//(][ meterCoulombNewtonsB
gausssmCNewtonmwteslaT 42 10//1/1)(1
TGaussBEarth4101
![Page 6: The Magnetic Field The force on a charge q moving with a velocity The magnitude of the force](https://reader035.vdocument.in/reader035/viewer/2022062216/56649d485503460f94a22e8f/html5/thumbnails/6.jpg)
left-hand ruleright-hand rule
![Page 7: The Magnetic Field The force on a charge q moving with a velocity The magnitude of the force](https://reader035.vdocument.in/reader035/viewer/2022062216/56649d485503460f94a22e8f/html5/thumbnails/7.jpg)
Motion in magnetic field
1) Uniform , B
Bv
2) Uniform , B
Bv
3) Nonuniform B
![Page 8: The Magnetic Field The force on a charge q moving with a velocity The magnitude of the force](https://reader035.vdocument.in/reader035/viewer/2022062216/56649d485503460f94a22e8f/html5/thumbnails/8.jpg)
0E
BvqF
![Page 9: The Magnetic Field The force on a charge q moving with a velocity The magnitude of the force](https://reader035.vdocument.in/reader035/viewer/2022062216/56649d485503460f94a22e8f/html5/thumbnails/9.jpg)
qvBFBv
amF
0 FmaF rr
r
vmmrqvB
22 ri
qB
mvr
The angular velocity
m
qB
qBmvv
r
v
0|| FBv
![Page 10: The Magnetic Field The force on a charge q moving with a velocity The magnitude of the force](https://reader035.vdocument.in/reader035/viewer/2022062216/56649d485503460f94a22e8f/html5/thumbnails/10.jpg)
The angular velocity (cyclotron frequency )
m
qB
qBmvv
r
v
2
f
does not depend on velocity!
The force is always perpendicular to velocity, so it cannot change the magnitude of the velocity, only its direction. The work done by the magnetic force is zero! Motion of a charged particle under the action of a magnetic field alone is always motion with constant speed.
![Page 11: The Magnetic Field The force on a charge q moving with a velocity The magnitude of the force](https://reader035.vdocument.in/reader035/viewer/2022062216/56649d485503460f94a22e8f/html5/thumbnails/11.jpg)
Electron motion in a microwave oven
A magnetron in a microwave oven emits electromagnetic waves with frequency f=2450 MHz. What magnetic field strength is required for electrons to move in circular paths with this frequency?
![Page 12: The Magnetic Field The force on a charge q moving with a velocity The magnitude of the force](https://reader035.vdocument.in/reader035/viewer/2022062216/56649d485503460f94a22e8f/html5/thumbnails/12.jpg)
Using Crossed and Fields E
B
Velocity selector
0 qEqvB
vBE
B
Ev independent of the mass of the particle!
![Page 13: The Magnetic Field The force on a charge q moving with a velocity The magnitude of the force](https://reader035.vdocument.in/reader035/viewer/2022062216/56649d485503460f94a22e8f/html5/thumbnails/13.jpg)
Mass spectrometer
qB
vmR 1
1
B
Ev
21
1 qB
EmR
22
2 qB
EmR
![Page 14: The Magnetic Field The force on a charge q moving with a velocity The magnitude of the force](https://reader035.vdocument.in/reader035/viewer/2022062216/56649d485503460f94a22e8f/html5/thumbnails/14.jpg)
Thomson’s e/m experiment
1897: Cavendish Laboratoryin Cambridge, England
m
eVveVmv
2
2
1 2
B
Ev
2
2
2
2
VB
E
m
e
m
eV
B
E
![Page 15: The Magnetic Field The force on a charge q moving with a velocity The magnitude of the force](https://reader035.vdocument.in/reader035/viewer/2022062216/56649d485503460f94a22e8f/html5/thumbnails/15.jpg)
Current carrying wires
1820 Hans Christian Oersted
Hans Christian Ørsted
![Page 16: The Magnetic Field The force on a charge q moving with a velocity The magnitude of the force](https://reader035.vdocument.in/reader035/viewer/2022062216/56649d485503460f94a22e8f/html5/thumbnails/16.jpg)
Gauss’s Law
The total flux of electric field out of any closed surface is equal to the charge contained inside the surface divided by .0
S
enclosedQSdE
0
![Page 17: The Magnetic Field The force on a charge q moving with a velocity The magnitude of the force](https://reader035.vdocument.in/reader035/viewer/2022062216/56649d485503460f94a22e8f/html5/thumbnails/17.jpg)
Conductors and insulators
Charges reside at the surface of the conductor
Conductor
E=0+
+ ++
+
+++
++
+++
+
+
![Page 18: The Magnetic Field The force on a charge q moving with a velocity The magnitude of the force](https://reader035.vdocument.in/reader035/viewer/2022062216/56649d485503460f94a22e8f/html5/thumbnails/18.jpg)
Electric field of a ball of charge
30
20
4
1
4
1
R
rQERr
r
QERr
Q
Electric field outside of a charged sphere is exactly the same as the electric field produced by a point charge, located at the center of the sphere, with charge equal to the total charge on the sphere.
![Page 19: The Magnetic Field The force on a charge q moving with a velocity The magnitude of the force](https://reader035.vdocument.in/reader035/viewer/2022062216/56649d485503460f94a22e8f/html5/thumbnails/19.jpg)
Insulating sphere with charge Q uniformly spread throughout the volume
A
E
r
204
1
r
QEAr
rA
QEAr
304
A
![Page 20: The Magnetic Field The force on a charge q moving with a velocity The magnitude of the force](https://reader035.vdocument.in/reader035/viewer/2022062216/56649d485503460f94a22e8f/html5/thumbnails/20.jpg)
Conducting sphere with charge Q
A
E
r
204
1
r
QEAr
0 EAr
V
r
A
A
Q
04
1
r
QVAr
04
1
A
QVAr
04
1
![Page 21: The Magnetic Field The force on a charge q moving with a velocity The magnitude of the force](https://reader035.vdocument.in/reader035/viewer/2022062216/56649d485503460f94a22e8f/html5/thumbnails/21.jpg)
A Charged, Thin Sheet of Insulating Material
++
+
+
++
+
++
++
02
E
![Page 22: The Magnetic Field The force on a charge q moving with a velocity The magnitude of the force](https://reader035.vdocument.in/reader035/viewer/2022062216/56649d485503460f94a22e8f/html5/thumbnails/22.jpg)
A field in a cavity of a conductorFaraday’s cage
![Page 23: The Magnetic Field The force on a charge q moving with a velocity The magnitude of the force](https://reader035.vdocument.in/reader035/viewer/2022062216/56649d485503460f94a22e8f/html5/thumbnails/23.jpg)
Electric field near a surface of a conductor
al
cap
EaEdSSdE
0a
Ea 0
E
![Page 24: The Magnetic Field The force on a charge q moving with a velocity The magnitude of the force](https://reader035.vdocument.in/reader035/viewer/2022062216/56649d485503460f94a22e8f/html5/thumbnails/24.jpg)
A
QLL
A
ALbottomVtopV
000
)]()([
0AQL
V
The capacitance is:
L
A
AQLQ
V
QC 0
0
Spherical capacitor; Cylindrical capacitor
![Page 25: The Magnetic Field The force on a charge q moving with a velocity The magnitude of the force](https://reader035.vdocument.in/reader035/viewer/2022062216/56649d485503460f94a22e8f/html5/thumbnails/25.jpg)
Capacitors in series: ...1111
321
CCCCtot
Capacitors in parallel: ...321 CCCCtot
22
2
1
2
1Q
CCVW
faradC ][
If the capacitors were initially uncharged,
![Page 26: The Magnetic Field The force on a charge q moving with a velocity The magnitude of the force](https://reader035.vdocument.in/reader035/viewer/2022062216/56649d485503460f94a22e8f/html5/thumbnails/26.jpg)
Current Density
S
Sdji
Consider current flowing in a homogeneous wire with cross sectional area A.
jAdSjjdSSdjiA A A
A
ij for j =Const only!
![Page 27: The Magnetic Field The force on a charge q moving with a velocity The magnitude of the force](https://reader035.vdocument.in/reader035/viewer/2022062216/56649d485503460f94a22e8f/html5/thumbnails/27.jpg)
Current, Ohm’s Law, Etc.
dt
dQi
)(;:' VoftindependenConstRi
VRLawsOhm
A
lR
Ej
jE
![Page 28: The Magnetic Field The force on a charge q moving with a velocity The magnitude of the force](https://reader035.vdocument.in/reader035/viewer/2022062216/56649d485503460f94a22e8f/html5/thumbnails/28.jpg)
For steady state situation
1.Kirchhoff’s junction rule: The algebraic sum of the currents into any junction is zero.
2.Kirchhoff’s loop rule: The algebraic sum of the potential differences in any loop must be zero.
0 Sdj
0 rdE
![Page 29: The Magnetic Field The force on a charge q moving with a velocity The magnitude of the force](https://reader035.vdocument.in/reader035/viewer/2022062216/56649d485503460f94a22e8f/html5/thumbnails/29.jpg)
Joule’s Law
R
VRiViP
22
![Page 30: The Magnetic Field The force on a charge q moving with a velocity The magnitude of the force](https://reader035.vdocument.in/reader035/viewer/2022062216/56649d485503460f94a22e8f/html5/thumbnails/30.jpg)
Resistors in parallel:
Resistors in series:
21 RRR
21
111
RRR
![Page 31: The Magnetic Field The force on a charge q moving with a velocity The magnitude of the force](https://reader035.vdocument.in/reader035/viewer/2022062216/56649d485503460f94a22e8f/html5/thumbnails/31.jpg)