Electromagnetic Induction

Chapter 20

1831 Faraday (England) & Henry (US) found that if a conductor is located in a changing magnetic flux, an induced emf will be created in the conductorIf conductor makes complete circuit, induced current will result
Changing flux can be result of motion between conductor and magnetic field or changing magnetic field strength
Only motion perpendicular to lines of flux will induce emf
Magnitude of emf depends on rate of change of flux

Negative sign means induced emf is in a direction opposite to the change that created it: this is Lenz's Law
If flux is decreasing, induced emf will be in a direction to produce a supporting magnetic field
If flux is increasing, induced emf will produce an opposing magnetic field

Force on a charge Q, moving at speed v, in magnetic field of flux density B; F = QvB
Force is always perpendicular to velocity.
Therefore, it can't change speed, only direction of velocity - creates centripetal acceleration and circular motion

Consist of a conducting loop rotated in magnetic field which induces current in the loop
Electrical contact is made with an external circuit through slip rings and brushes
Converts mechanical energy to electrical
Many coils are usually combined into an armature
Direction of electron flow in armature coil will create force that opposes coil rotation (Lenz's law)
Use left hand generator rule to find direction of current: pointer finger in direction of magnetic field, thumb in direction of coil rotation, middle finger shows direction of electron flow.

AC current pushes electrons back and forth with alternating positive and negative emf
This occurs because the rotating coil cuts lines of flux first in one direction, then in opposite
Potential varies between maximum values of ± E and has instantaneous value of e that varies sinusoidally depending on the angle of armature with the magnetic field
Maximum emf (E_max) generated when coil is perpendicular to magnetic field
e = E _max sinθ
Current will vary in the same way
i = I_maxsinθ
Magneto is generator that uses permanent magnets, used on small gasoline engines
Larger generators use electromagnets supplied by separate dc current called exciter
These larger generators usually reverse the relationship between armature and field coils using a stator (stationary armature) and rotor (rotating field coils)

To supply dc (current in one direction) armature coils are connected to a commutator that reverses the connection to the external circuit at the point when the induced emf changes direction. This produces a pulsed dc that can be made smoother with many coil windings.
The field is self-exciting - it uses part of the generator output to excite the field coils (electromagnets)
The field can be connected in series (series wound), in parallel (shunt wound), or a series/parallel combination with the armature and the load. The load is a general term for whatever is in the external circuit drawing current from the generator.

Armature windings act like battery internal resistance - create potential drop: V_out= E - I_Ar_AUse Ohm's law to figure currents and voltage drops across field or load resistances
Power output: P_T = EI_A= P_A + P_F + P_L or E I_A= I_A²R_A + I_F²R_F + I_L²R_L where subscript A refers to the armature, subscript F refers to the field, and subscript L refers to the load.

Motors have the same parts but operate in reverse of generators
Current through a coil in magnetic field creates a force that tries to expel the coil from the magnetic field
Equal but opposite forces on opposite sides of the coil (a force couple) create torque that turns the coil
Force is at a maximum when the conductor moves perpendicular tothe magnetic field
Magnitude of the torque is the product of the force times the coil width: T_max= Fw
When coil is at an angle alpha with the field: T = Fw cosα
To keep armature from being held in zero torque position, current direction must be reversed at the proper time using a commutator
To find the direction of the force on the coil and the subsequent motion, use the right hand motor rule: pointer finger in direction of field, middle finger in direction of electron flow through coil, thumb points in direction of motion

Since a motor is a conductor moving in magnetic field, it will generate emf that opposes the emf applied to the motor
Amount of back emf depends on the speed of armature rotation
Difference between applied voltage and back emf determines the current in the motor circuit
At full speed and no load, back emf almost equals applied voltage and so a small current results in the motor circuit
With a heavy load, back emf decreases and current rises
At slow speed, back emf is low and current is high

Universal motor - small series type; can use ac or dc. Most small electric motors are of this type.
Induction - uses rotor and stator with slotted, laminated iron core; needs separate starting circuit. Most large electric motors are of this type
Synchronous motor - constant speed synchronized with 60 Hz ac supply frequency. Speed does not depend on supply voltage but frequency.

Created by conductor in changing magnetic field
Change can be due to relative motion between conductor and magnetic source or from collapsing/expanding field

Change in current through onecoil will induce an emf in a nearby coil
symbol M, unit is also henry
Mutual inductance = the ratio of induced emf in one coil (secondary) to rate of change of current in the other (primary)

Circuit elements with specific inductance whose function is to store energy in a magnetic field
Similar to capacitors storing energy in electric fields
Equivalent inductance of combinations of inductors are found using the same rules for equivalent resistance

Two coils wound on same iron core
Electric energy is transferred through magnetic flux in the core from one coil to the other
AC current through primary coil induces alternating emf in secondary
Ratio of voltages in each coil = ratio of the number of turns in each coil
V_S/ V_P = N_S/ N_P where subscript S means secondary coil and subscript P means primary coil, N = number of turns in each coil
For current: I_SN_S=I_PN_P ; if we assume an ideal transformer with no losses
Actual efficiency is high but not 100% in a real transformer. Efficiency = P_S/P_P x 100%
Losses due to resistance of coil wires - copper losses - and to eddy currents in iron core
A laminated core reduces eddy current losses, losses due to wiring resistance cannot be eliminated

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