Electromagnetic Induction: Faraday's Law and Lenz's Law, Slides of Physics

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Chapter 1

Electromagnetic induction

Chapter 6

Faraday’s experiment

Faraday discovered electromagnetic induction. When the current was steady, the galvanometer indicated no induced current, but when the switch was turned on or off – and only then – was an induced current measured. In 1831, Faraday used the experiment below to test his hypothesis that a magnetic field would induce an electric current. Changing the current produces a variation in the magnetic field associated with the current. A changing magnetic field therefore induces an electromotive force (EMF) which produces an induced current.

Faraday and Neumann’s law of induction

The induced EMF in a wire loop is proportional to the rate of change of the magnetic flux through the surface associated with the loop. The unit of magnetic flux is the weber, Wb: 1 Wb = 1 T ∙ m^2. The magnetic flux through a loop is proportional to the total number of magnetic field lines passing through the loop. where is the flux through the surface. where θ is the the angle between the magnetic field vector and the vector , normal to the loop of area A.  fem  

r

^ B 

 t 

r B )  r B

r

A

r

^ B ^

r B  r A    BA cos (^)  

Lenz’s law

magnitude of the external magnetic field, B flux of the external magnetic field, B external magnetic field B lines direction of the induced magnetic field, B i increase more numerous opposite to B decrease less numerous same as B The current produced by an induced EMF moves in such a direction that the magnetic field it produces attempts to restore the changed field to its original value. An induced EMF is always in a direction that opposes the original change in flux that caused it.

r

B )  0

r

B )  0

force on a rod moving in a magnetic field

The external force needs to be equal and opposite to the magnetic force F = IB. The induced current is equal to the change in the flux, divided by the resistance R of the loop. Hence the external force to be applied is:

l

Moving a rod, that is part of a conducting loop, inside a megnetic field, generates current. To make the rod move to the right at speed v , an external force needs to be applied on the rod to the right, as the system attempts to restore the changed flux (Lentz’s law). 

I 

B l v R F 

B

2 l 2 v R

alternating current

The motion of a metal loop within a magnetic field causes electrons to move in the metal, under the influence of Lorentz forces, thereby generating a current. If the loop is rotating with a constant velocity in a uniform magnetic field, an alternating current is generated The voltage varies sinusoidally with time: where V 0 is the peak voltage, i.e. the amplitude of the oscillation, f is the oscillation frequency and ω is the angular frequency, i.e. ω = 2π f.

V  V 0 sin (^)  2  f t  V 0 sin (^)  t  

I 

V

R

V 0

R

sin (^)  t  I 0 sin (^)  t 

the Earth’s magnetic field

The direction of the Earth’s magnetic field is titled by 11.5 degrees with respect to its rotational axis. The Earth's magnetic field can be approximated as a dipole field at the Earth’s surface. However due to solar winds it is distorted further out. Moving electric charges generate magnetic fields and varying magnetic fields move charges. In the core of the Earth, metal ions are in movement, dragged by Earth’s rotation. Metal ions in movement give rise to a current that produces the Earth’s magnetic field.

learning the basics

1. An induced EMF is generated when a steady magnetic field is placed inside a metal loop. T F 2. A current produced by an induced EMF moves in such a direction that the magnetic field it produces attempts to restore the changed field to its original value. T F 3. The Earth’s magnetic field is due to the magnetic property of the matter inside the Earth’s core. T F j^ j jj j^ j jj j^ j

applying the concepts

2. Draw the direction of the normal surface vector and complete the figure with the missing values and formulas.

r

A