1. Lectures 15&16 : The Laws of Electromagnetic Induction
Learning Objectives
To introduce the concept of electromagnetic induction and to illustrate that electric fields can be generated not only by charges but by changing magnetic fields
To look at the concept of magnetic flux linkage
To illustrate how the magnitude of an induced voltage can be calculated
To list the laws of electromagnetic induction

2. - + E = vB                        
Electromagnetic Induction             - +
Conducting Rod length l
FB=evB
FE=eE e-             v
E = vB
Electrons accumulate until FE = FB
Get an induced voltage  across the ends of the conductor
In equilibrium  = El = vBl

3. Rate of work done by induced voltage =  I l B F
Force on wire is: F = BIl v
To maintain motion a force of equal magnitude must be applied in the direction of v - Rate of work = Fv = BIlv
Rate of work done by induced voltage =  I
 = Blv

4. 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

5. Ways of Expressing the Induced emf
In a time dt the conductor sweeps out an area lvdt. The flux cut by the conductor in time dt is:
The induced voltage is equal to the rate of change of flux-linkage
Magnitude of emf
Faraday’s First Law:
When the magnetic flux threading a circuit changes, a voltage is induced in the circuit
Faraday’s Second Law:
The magnitude of an induced voltage is proportional to the rate of change of flux- linkage

6. 1. 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.
2. 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.

8. 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 gave rise to the current
Motion of Magnetic Fields thus gives rise to Electric Fields

9. E B
An induced voltage 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

10. Maxwell’s Third Law of Electromagnetism
A time varying magnetic field induces a non-conservative electric field loop.
And
Further
Classwork: 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.

11. 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.