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Magnetic Field Sources
Magnetic Fields
• A force field that denotes the area in which the non-contact force of permanent magnets or current carrying conductors can exert their influence
• Fields are concentrated at the poles
• Same properties with Electric field lines except that there is no magnetic monopole
Magnetic field lines
Magnetic Force
• Like poles repel, opposite attract
• An object that contains iron but is not itself magnetized is attracted by either pole of a permanent magnet.
Magnetic Force
Magnetic interactions can be described as:
• A moving charge or a current creates a magnetic field in the surrounding space (in addition to its electric field)
• The magnetic field exerts a force Fm on any other moving charge or current that is present in the field.
• The magnetic force Fm acting on a positive charge q moving with velocity v is perpendicular to both Fm and the magnetic field B.
Units of Magnetic Fields
• SI units: tesla, T1 tesla = 1 T = 1 N/A·m
• Or: gauss, G1 G = 10-4 T
Magnetic Force on Moving Charge• Moving charged particles are deflected in magnetic
fields
• Right-Hand Rule
F q v B
Grip and Hand Rules
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The magnetic force is always perpendicular to v; a particle moving under the action of a magnetic field alone moves with a constant speed.
Magnetic Force on Moving Charge
Motion of charged particles in a magnetic field
Motion of charged particles in a magnetic field
Fig. 27.18
Motion of charged particles in a magnetic field
Fig. 27.17
Applications of motion of charged particles
Velocity Selector• Particles of a specific
speed can be selected from the beam using an arrangement of electric and magnetic fields called a velocity selector.
Magnetic Force on Current Carrying Wire
sinIlBF
BIlF
M
M
Magnetic Force on Current Carrying Wire
Ampere’s Law
enclosedIlB 0
• Used to determine the magnetic field yielded by current-carrying wire
• Ampere’s law states that the product B and length of line segment around any closed path equals µ0 times the net current through the area enclosed by the path.
• Direction of Magnetic field is determined by corkscrew method
Ampere’s LawB=0I/2L
Magnetic field profile of 2 parallel current carrying wires
Solution
)P (point
)P (point
)P (point
3
2
1
dI
dI
dI
BBB
dI
dI
dI
BBB
dI
dI
dI
BBB
total
total
total
362
22
884
00012
00021
00021
Magnetic Field in Solenoid
Magnetic Field in SolenoidB=0nI
Ampere’s Experiment
B1=0I1/2L F= 0I1I2l/2L
Exercise
B1=0I1/2L F/l= 0I1I2/2L
ExampleSuspending a current with a current
A horizontal wire carries a current I1=80 A dc. A second parallel wire 20 cm below it must carry how much current I2 so that it doesn’t fall due to gravity? The lower wire is a homogenous wire with a mass of 0.12 g per meter of length.
F/L = mg/L=1.18 x 10-3 N/m
0I1I2/2 L = 1.18 x 10-3 N/m
I2= 15 A
Definitions
• Ampere current flowing in each of the two long parallel conductors 1 m apart, which results in a force of exactly 2 x 10-7 N/m of length of each conductor.
• Coulomb one ampere-second
Solution Set
F/l= 0I1I2/2L
FA/l= 5.83 x 10-5N/m; 90
FB/l=3.37 x 10-5N/m; -60
FC/l=3.37 x 10-5N/m; 240
