Principles of Electromechanics

Electricity Motion

Electricity Motion: MotorMotion Electricity: Generator

Magnetic Field & Faraday’s Law

Magnetic Field

1. Generation of magnetic field• Permanent Magnet: • Electric Current: using right hand

rule to determine the field direction• Straight current• Current coil

N

S

Current Motion: Current in magnetic field

• Magnetic field will exert a force on a current

• Magnetic field will exert a force on a moving charge

(N/m) BIL

F

× × × × × × × × × × × ×× × × × × ×× × × × × ×× × × × × ×× × × × × ×× × × × × ×

I

F

× × × × × × × × × × × ×× × × × × ×× × × × × ×× × × × × ×× × × × × ×× × × × × ×

-qV

FrqVB

qVBF

BVqF

B

B

sin

Circular Motion: Plane B

× × × × × × × × × × × ×× × × × × ×× × × × × ×× × × × × ×× × × × × ×× × × × × ×

-qV

Fr

Circular path: V||=0 Helical path: V||0

Charges in B field: Applications

Mass Spectrometer:Cyclotron (accelerator)

Example: Rail Gun

Acceleration: 5 106 gFinal speed: 1 km/sDuration: 1 ms

Motion Current: Generating Electricity (Faraday’s law)

1. A current appears only if there is relative motion.

2. Fast motion produces a greater current.

3. Clockwise/counter clockwise current with north pole move in/out. Opposite with south pole.

Induced current in secondary coil, if there is change of current in the primary coil: switch or ac current

Transformer

Faraday’s Law of Induction

Magnetic flux through area A

Amount of magnetic field passes through an area A

Faraday’s Law of Induction: An emf is induced in a loop when the magnetic flux that pass through the loop is changing. The the loop is conducting, then a current will flow.

AdBB

For uniform B: cosBAB (Weber, or Wb, or T m2

dt

d B For a loop with N turns: dt

dN B

Change B (change current) Change A Change angle between them

Current loop in magnetic field: Motors

B B•

F

F

L

iLBF

iBA

iBLwFw

Fr

22

•

w

Torque on a Current Loop: Motors

B•

F

F

B•

F

F

B•

F

F

sin

sin2

2

iBA

Fw

iBA

n

n

n

0

Torque on a Current Loop: Continuous

siniBAiBA

B•

F

F

n

B•

F

F

n

B

•

F

F

0

B

•

FF

B

•

F

F

n