ELECTROMAGNETIC INDUCTION Electric fields are produced by electric charges: Electrostatics. Electric fields can also be produced by a changing magnetic field:electromagnetic induction

Physics for Scientists and Engineers Paul A. Tipler • Gene Mosca Physics for Scientists and Engineers Fifth Edition Chapter 28: Magnetic Induction Copyright © 2004 by W. H. Freeman & Company

Learning Aims To illustrate that electric fields can be generated not only by charges but also by changing magnetic fields To show that these induced electric fields can be used to drive currents in electrical circuits

Learning Outcomes To understand the concept of electromagnetic induction – producing an induced voltage – To understand the physical properties which determine the size of an induced voltage – Faraday’s Law To understand that energy conservation allows us to deduce the polarity of an induced voltage – Lenz’s Law

Lecture observation For me, Business as usual For you: 1. Pretend as though you are naturally interested in the topic. 2. From time to time, gesturing to your friends that you feel excited about the physics. 3. Sleep with your eyes open please. 4. Raise your hands when I ask you a question.

Magnetic Field Lines the number of field lines drawn per unit cross sectional area is proportional to the magnitude of B the tangent to a field line at a point P gives the direction of B at that point

Magnetic Flux A The magnetic flux B passing through the small area A shown is defined by:

Hans Christian Oersted (1777-1851) In 1820 Oersted demonstrated that a magnetic field exists near a current-carrying wire - first connection between electric and magnetic phenomena. Electrostatics and magnetism were two different subjects until Oerted observed the connection between electrical current and magnetic field.

So, an electric current can generate a magnetic field. A great British scientist thought that the reverse might be possible – to generate electricity from magnetism.

Michael Faraday 1791 - 1867 Central to our study is the pioneering work of the British scientist Faraday. He discovered that whenever magnetic field lines move or change in anyway, they induce an electric field. This kind of electric field exerts the usual forces on charges – but it does not have its origin in charged particles! The unit for capacitance was named after Faraday

Moving Conductors Use Lorentz force law  to v and B in direction of E

- +                         The Motion of a Conductor in a B Field             B - + Conducting Rod length l FB=evB FE=eE e- v             Electrons accumulate until FE = FB Get an induced voltage  across the ends of the conductor

E = vB  In equilibrium Potential difference induced  = El = vBl v FB=evB FE=eE E = vB In equilibrium Potential difference induced  = El = vBl

Question: If we can generate a potential difference across a rod, is it possible to use this to light up a bulb? YES!

I              v The moving rod has become a source of electrical energy  The ends of the rod are in sliding contact with a pair of wires, a current will flow around the circuit

 B F Force on wire is: F = BIl v To maintain motion at constant speed a force of equal magnitude must be applied in the direction of v - Rate of work = Fv = BIlv

Rate of work done by electrical energy Conservation of Energy BIlv =  I  = Blv

This can be given an interesting interpretation in terms of the MAGNETIC FLUX In a time dt the rod travels a distance vdt l  lvdt Area Change B

Magnitude of Induced Voltage In a time dt the conductor sweeps out an area lvdt. The flux change in time dt is: Magnitude of Induced Voltage

Linking the Induced Voltage with FB Magnitude of induced voltage is equal to the rate of flux change Faraday’s Law of Electromagnetic Induction The unit for magnetic flux: 1 weber= 1Wb= 1 T m2

Note, that an induced voltage can be a result of a change in area or magnetic field, or both!  B

B=B0sinwt Area=pr2 l FB= pr2 B0sinwt

people use “induced electromotive force” (emf) people use “induced electromotive force” (emf). This is a misconception - the quantity involved is not a force. The quantity is a potential difference.

Production of Electricity Major Application Production of Electricity Conversion of one form of energy (e.g. gravitational, chemical, nuclear) to electric energy

Summary of the Laws of Electromagnetic Induction (so far) What about the direction of the induced voltage?

The Polarity of an Induced Voltage S N The motion induces a voltage and hence a current in the metal ring. The current produces a magnetic field so that the ring behaves like a bar magnet. Question: The B-field from the induced current repels the approaching magnet, Yes or no? Would the forces differ if the magnet were moving away from the metal ring?

It’s all to do with conservation of energy! The Laws of Electromagnetic Induction (continued) Lenz’s Law: The direction of an induced current (if one were to flow) is such that its effect would oppose the change in magnetic flux which give rise to the current It’s all to do with conservation of energy!

The magnetic field generated can only hinder the motion The magnetic field generated can only hinder the motion. Helping the motion would result in the creation of a perpetual motion machine, which violates the conservation of energy.

Mathematically

E B The electric field associated with an induced voltage. A non-conservative E-field.

Faraday’s Law of Electromagnetic Induction ò = - E . d l B dt A time varying magnetic field induces a non-conservative electric field loop.

Review and Summary An induced electric field is present even if the loop through which a magnetic flux is changing is not a physical conductor but an imaginary line. A changing flux induces a non-conservative E-field at every point of such a loop.

Relative movement of a wire through a magnetic field (start with the Lorentz Equation) Changing the magnetic field strength around a wire Induced current if wire forms part of a complete circuit – the faster the changes, the larger the current.

Learning outcome: You should be able to 1. Use Faraday’s Law of electromagnetic induction to calculate the magnitude of an induced voltage 2. Use Lenz’s law to determine the polarity (direction) of an induced voltage and hence the direction of an induced current in a circuit A4

(Ans. 0.27 V (comment on the size of this!)) Student Exercise A Stealth aircraft is diving vertically downwards at Mach 5 in a region where the speed of sound is 330 m s-1 and the Earth’s horizontal magnetic field is 20.6 micro Tesla. Calculate the magnitude of the voltage induced between the wing tips, 8.0 m apart, if the wings point east-west. Mach 5 means a speed 5 times the (local) speed of sound (Ans. 0.27 V (comment on the size of this!))

Student Exercise A uniform magnetic field makes an angle of 30O with the axis of a circular coil of 300 turns and a radius of 4 cm. The field changes at a rate of 85 T/s. Find the magnitude of the induced voltage in the coil. First “picture the problem” – the induced voltage equals N (=300) times the rate of change of flux through each turn. Since B is uniform, the flux through each turn is simply BAcos where A is the area of the coil. (Ans. 111 V)

Components in electric circuits Resistance R: R= V/I Capacitance C: C=Q/V Inductance: L: L=f/I

This lecture provides principles that we need to understand electrical energy conversion devices, including motors, generators, and transformers. It also paves the way to the understanding of electromagnetic radiation.

E-field generated whether or not there is a conducting loop Suppose we remove the conducting ring, and change the magnetic field. Will there be an electric field induced?!! YES! E-field generated whether or not there is a conducting loop This raises another very interesting question . . . . .can a changing electric field produce a magnetic field? James Clerk Maxwell 1831-1879 YES!

A Changing Magnetic Field Creates an Electric Field (Electromagnetic Induction) A Changing Electric Field Creates a Magnetic Field Light is an electromagnetic wave – a wave made up of oscillating electric and magnetic fields – electromagnetic waves are self-propagating!

Thus thanks to electromagnetic induction we can “see” the Universe

Review and Summary The Laws of Electromagnetic Induction = =

Self and Mutual Inductance Next Topic Self and Mutual Inductance