Eleanor Roosevelt High School Chin-Sung Lin Lesson 21

 In 1831, Michael Faraday (England) and Joseph Henry (US) independently discovered that magnetism could produce current in a wire

Faraday’s law— Electromagnetic induction  Electromagnetic induction— any change in the magnetic field around a conductor induces a voltage (or emf)  Faraday’s law— The induced voltage (or emf) in a coil is proportional to the product of the number of loops and the rate of change of the magnetic field within those loops

How can we change the magnetic field around a conductor to induces a voltage (or emf)?

 The change could be produced by ◦ relative motion of a wire with respect to the magnetic field

 The change could be produced by ◦ moving the coil into or out of the magnetic field

 The change could be produced by ◦ rotating the coil relative to the magnet

 The change could be produced by ◦ changing the magnetic field strength

 A magnet moving past a stationary conductor, or  A conductor moving through a stationary magnetic field

 The work done to the magnet is equal to the energy generated in the circuit to which the coil is connected W mechanical = W electric

 Induced voltage depends on: ◦ Speed of the wire traversing the magnetic field lines. Quicker motion induces a greater voltage (V ~ v ) ◦ Number of loops of wire that moves in a magnetic field. The voltage is proportional to the number of loops (V ~ N)

 If the coil does not form a complete circuit, what will happen?

 Induced voltage without current, no work to plunge the magnet into the coil - +

 If the coil forms a complete circuit, what is the direction of the induced current? A Ammeter

 The induced magnetic field is repelling, the current will flow in a way to create such a repelling field A Ammeter

 The more loops of the coil, the more voltage induced (V ~ N)  The more voltage induced in the coil, the more current through the resistor in the circuit (I ~ V)  The more current through the coil, the stronger the magnetic field it generated (B ~ I)  The stronger the magnetic field generated, the stronger the repelling force acting back to your magnet (F ~ B)  A coil with more loops is a stronger electromagnet and push back harder

 What factors will affect the induced current? A Ammeter

 Induced current depends on ◦ the induced voltage ◦ the resistance of the coil and the ◦ the “reactance” of the coil Ammeter A

 Reactance ◦ similar to resistance ◦ depends on  the number of loops in the coil  the frequency of the AC source

 Reactance The counter-emf is the source of the opposition to current flow change ◦ A constant DC current has a zero rate-of- change, and sees an inductor as a short- circuit ◦ An AC current has a time-averaged rate- of-change that is proportional to frequency, this causes the increase in inductive reactance with frequency

 Induced voltage of a moving conductor in a magnetic field V = v B L

 The movement of a magnet is alternating, the induced voltage alternates on direction  The greater the frequency of the field change, the greater the induced voltage

 The frequency of the induced alternating voltage equals the frequency of the alternating magnetic field within the loops High Frequency Low Frequency

 Generator— a device that converts mechanical energy to electrical energy  Motor— a device that converts electrical energy to mechanical energy

 When a closed conductor loop is moved in a magnetic field, an induced current flows through it  The direction of induced current is given by the Flemming's right hand generator rule

 What’s the direction of the induced current? N S

 Given by the Flemming's right hand generator rule N S

 As the number of magnetic field lines within the loop changes, the magnitude and direction of the induced voltage and current change

 One complete rotation of the loop produces on complete cycle in voltage and current

 The voltage induced by the generator alternates, and the current produced is alternating current (AC)  The standard alternating current is 60 Hz

 Hydro power generators

 One complete rotation of the loop produces on complete cycle in voltage and current

 A a static device that transfers electrical energy from one circuit to another through inductively coupled conductors  A static device that transfers electrical energy to magnetic energy, and to electric energy again  A device with which we can raise (for transmission) and lower (for use) the AC voltage in a circuit  Transformer only works for AC

Primary Secondary  Primary and secondary coils  Use AC voltage source (primary coil)  AC voltage is induced (secondary coil)  Frequency AC voltage source = Frequency Induced AC voltage

 Iron core (high permeability) is inserted into the coils to intensify the magnetic field  Iron core forms a complete loop to guide all magnetic field lines through the secondary

 Transformer Symbol:

N p no. of turns of primary coil N s no. of turns of secondary coil V p voltage of primary coil V s voltage of secondary coil I p current of primary coil I s current of secondary coil IPIP ISIS

IPIP ISIS V P V S N P N S =

 Step-up transformer ◦ N P < N S ◦ V P < V S  Step-down transformer ◦ N P > N S ◦ V P > V S

IPIP ISIS P P = P S I P V P = I S V S

 V P / N P = V S / N S  I P V P = I S V S  V P / V S = I S / I P = N P / N S  V S = V P (N S / N P )  I S = I P (N P / N S ) V P I S N P V S I P N S = = NS NPNS NP V S = V P NP NSNP NS I S = I P

 Faraday’s law: ◦ An electric field is created in any region of space in which a magnetic field is changing with time ◦ The magnitude of the created electric field is proportional to the rate at which the magnetic field changes ◦ The direction of the created electric field is at right angles to the changing magnetic field

 Maxwell’s law: ◦ A magnetic field is created in any region of space in which an electric field is changing with time ◦ The magnitude of the created magnetic field is proportional to the rate at which the electric field changes ◦ The direction of the created magnetic field is at right angles to the changing electric field

 In 1861 Scottish physicist James Clerk Maxwell discovered the theory of electromagnetism  Maxwell united all previously unrelated observations and equations of electricity, magnetism and optics into a consistent electromagnetic field theory

 German physicist Heinrich Rudolf Hertz was the first to satisfactorily demonstrate the existence of electromagnetic waves by building an apparatus to produce and detect VHF or UHF radio waves

 A charge oscillates back and forth in empty space will produce electromagnetic waves in space where vibrating electric and magnetic fields regenerate each other

 Electric field is perpendicular to the magnetic field, and both are perpendicular to the direction of the motion of the wave

 No medium is required  The speed— the speed of light  The wave is continuously self-reinforcing. The changing electric field induced a magnetic field. The changing magnetic field acts back to induce a electric field