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class="gray">Faraday's law</span></li> <span class="pull-right" style="color: #555" title="Suggested study time: 20 minutes"><i class="fa fa-clock-o"></i> 20'</span> </ol> <article id="main-article"> <p><img alt="" src="../../em-induction/faraday.jpg" style="float: left; width: 200px; height: 250px;">In the SL Magentism course, you will have studied the motor effect, in which a current-carrying conductor or moving charge experiences a force in a magnetic field.</p> <p>In the HL course, we move to electromagnetic induction. When a magnetic field is changed or moved relative to an electrical conductor, an EMF is induced. When the conductor is connected as part of a complete circuit, a current flows.</p> <p>Faraday's law enables us to calculate the size of the induced voltage. First we will need to define a new concept - magnetic flux.</p> <hr class="hidden-separator"> <div class="panel panel-turquoise panel-has-colored-body"> <div class="panel-heading"> <div> <p>Key Concepts</p> </div> </div> <div class="panel-body"> <div class="panel panel-has-colored-body panel-has-border panel-turquoise"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Electromagnetic induction</p> </div> </div> <div class="panel-body"> <div> <p>When a charge moves in a magnetic field, it experiences a force that is perpendicular to its velocity. This causes free charges to move in a circular path (NB: <a href="../265/centripetal-force.html" title="Centripetal force">Centripetal force</a>). The direction of this force can be determined using Fleming's left hand rule:</p> <p style="text-align: center;"><img alt="" src="../../em-induction/lefthandoutline.png" style="width: 250px; height: 182px;"></p> <p>However, when constrained to a linear electrical conductor (i.e. a metal wire), charges cannot follow a circular path. If the wire continues to move in a straight line, electrons all electrons will experience a force in the same direction and move. Now that the electrons are not distributed evenly throughout the conductor, the wire has an electric field across it (like a battery). An EMF has been produced, that would cause a current to flow if the wire was connected to a resistor in a complete circuit.</p> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-has-colored-body panel-has-border panel-turquoise panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Magnetic flux</p> </div> </div> <div class="panel-body"> <div> <p>Magnetic flux is defined as the product of the magnetic flux density (NB: magnetic field strength) and the perpendicular area of the field.</p> <p style="text-align: center;"><img alt="" src="../../em-induction/flux.jpg" style="width: 250px; height: 237px;"></p> <p style="text-align: center;"><span class="math-tex">\(\Phi=BA\cos\theta\)</span></p> <ul> <li><span class="math-tex">\(\Phi\)</span> is magnetic flux (Tm<sup>2</sup> or Wb)</li> <li><span class="math-tex">\(B \)</span> is magnetic flux density (T)</li> <li><span class="math-tex">\(A\)</span> is the area of the surface</li> <li><span class="math-tex">\(\theta\)</span> is the angle between the magnetic field lines and the normal (perpendicular) to <span class="math-tex">\(A\)</span></li> </ul> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/369633862"></iframe></div> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-has-colored-body panel-has-border panel-turquoise panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Faraday's law</p> </div> </div> <div class="panel-body"> <div> <p>Faraday's law states that the magnitude of the induced EMF is proportional to the rate of change of magnetic flux.</p> <p style="text-align: center;"><span class="math-tex">\(|\varepsilon |\propto{\mathrm{d}\Phi\over \mathrm{d}t}\)</span></p> <ul> <li><span class="math-tex">\(|\varepsilon |\)</span> is the magnitude of the induced EMF (V)</li> <li><span class="math-tex">\(\Phi\)</span> is the magnetic flux (Tm<sup>2</sup> or Wb)</li> <li><span class="math-tex">\({\mathrm{d}\Phi\over \mathrm{d}t}\)</span> is the rate of change of magnetic flux (Tm<sup>2</sup>s<sup>-1</sup> or Wb s<sup>-1</sup>)</li> </ul> <p>The magnitude of the induced EMF is equal to the rate of change of magnetic flux linkage, where magnetic flux linkage is the product of the number of turns on the conducting coil and the magnetic flux.</p> <p style="text-align: center;"><span class="math-tex">\(|\varepsilon |={\mathrm{d}N\Phi\over \mathrm{d}t}\)</span></p> <ul> <li><span class="math-tex">\(|\varepsilon |\)</span> is the magnitude of the induced EMF (V)</li> <li><span class="math-tex">\(N\Phi\)</span> is the magnetic flux linkage (Tm<sup>2</sup> or Wb)</li> <li><span class="math-tex">\({\mathrm{d}N\Phi\over \mathrm{d}t}\)</span> is the rate of change of magnetic flux linkage (Tm<sup>2</sup>s<sup>-1</sup> or Wb s<sup>-1</sup>)</li> </ul> <div class="magenta"> <p>Learners often find the differentiation symbols intimidating - but generally you won't need to consider instantaneous moments in a continually changng situation. Instead, think of the <em>rate of chage of flux linkage </em>as:</p> <p style="text-align: center;"><span class="math-tex">\({\text{final flux linkage }-\text{ initial flux linkage}}\over \text{time}\)</span></p> </div> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <p> </p> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Essentials</p> </div> </div> <div class="panel-body"> <div> <div class="panel panel-has-colored-body panel-has-border panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Moving wire</p> </div> </div> <div class="panel-body"> <div> <p>Instead of having a plane area within the field, the alternative is a length of wire that sweeps through it.</p> <p style="text-align: center;"><img alt="" src="../../em-induction/flux-moving-wire.jpg" style="width: 250px; height: 239px;"></p> <p style="text-align: center;"><span class="math-tex">\(\varepsilon=BLv\sin\theta\)</span></p> <ul> <li><span class="math-tex">\(\varepsilon\)</span> is the EMF induced (V)</li> <li><span class="math-tex">\(B \)</span> is magnetic flux density (T)</li> <li><span class="math-tex">\(L\)</span> is the length of wire (m)</li> <li><span class="math-tex">\(v\)</span> is the velocity of the wire (ms<sup>-1</sup>)</li> <li><span class="math-tex">\(\theta\)</span> is the angle between the magnetic field lines and the normal (perpendicular) to the swept out area</li> </ul> <p>The EMF induced is constant. A real-world example is a plane flying through the Earth's magnetic field!</p> <div class="magenta"> <p>The subject guide suggests that all cases of a wire moving through the field will be at <em>right angles</em>. But there's no harm in being prepared!</p> </div> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-has-colored-body panel-has-border panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Applications</p> </div> </div> <div class="panel-body"> <div> <h4>Generating electricity</h4> <p>Electromagnetic induction is the principle on which almost all methods for generating electricity are founded. All of the following contain a turbine that turns a coil relative to a magnetic field (or vice versa):</p> <ul> <li>Fossil fuel power stations</li> <li>Nuclear power stations</li> <li>Wind turbines</li> <li>Hydroelectric turbines</li> <li>Wave and tidal turbines</li> <li>Geothermal</li> </ul> <p>Check out <a href="../452/energy-sources.html" title="Energy sources">Energy sources</a> if you need a recap!</p> <h4>Other uses</h4> <p>The following devices use electromagnetic principles:</p> <ul> <li><a href="../1140/transformers.html">Transformers</a></li> <li>Electromagnetic braking - friction brakes (which dissipate kinetic energy as thermal energy) can be replaced by electromagnets (which convert the kinetic energy into electrical energy). A benefit is that these do not wear out and so do not require replacement.</li> <li>Geophones - seismic events cause a magnet to move relative to a coil. An inertial mass on a spring is connected rigidly either to the magnet or the coil to ensure that one remains stationary. The greater the magnitude of the earthquake, the greater the voltage induced.</li> <li>Metal detectors - when a current-carrying coil moves relative to a conductor beneath the ground, its magnetic field induces an EMF in the hidden conductor. The hidden conductor in turn becomes an electromagnet and exerts a force on the original coil.</li> </ul> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-green"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Test Yourself</p> </div> </div> <div class="panel-body"> <div> <p><em>Use flashcards to practise your recall.</em></p> <div class="tib-flashcard"><a class="show-flashcards btn btn-success btn-xs-block btn-block " data-levels="1,3" data-mode="" data-topics="1005" data-subject-id="6" data-n-flashcards="8" style="text-align:center">Show flashcards</a></div><hr> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-red"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Just for Fun</p> </div> </div> <div class="panel-body"> <div> <p>It is interesting, but not essential, to know how to derive Faraday's law. You should revise AHL electric potential beforehand.</p> <p>To do so, consider a metal wire. At the point at which the electric force acting on electrons (to return them to their evenly distributed state) is equal to the magnetic force (causing them to move to one side):</p> <p style="text-align: center;"><span class="math-tex">\(F_B=F_E\)</span></p> <p style="text-align: center;"><span class="math-tex">\(Bev=Ee\Rightarrow Bev={V\over L} e\)</span></p> <p style="text-align: center;"><span class="math-tex">\(V=BLv\)</span></p> <ul> <li><span class="math-tex">\(V\)</span> is the work done per unit charge against the electric force by the magnetic force (V)</li> <li><span class="math-tex">\(B\)</span> is magnetic flux density (T)</li> <li><span class="math-tex">\(L\)</span> is the length of the conducting wire (m)</li> <li><span class="math-tex">\(v\)</span> is the velocity at which the wire moves through the field (ms<sup>-1</sup>)</li> </ul> <p>Since the work done per unit charge in bringing the charges to their induced position is equal to that which would be released when a complete circuit is formed:</p> <p style="text-align: center;"><span class="math-tex">\(\varepsilon = BLv\)</span></p> <ul> <li><span class="math-tex">\(\varepsilon\)</span> is the induced EMF (V)</li> </ul> <p>Or if the wire is replaced by a coil with multiple turns:</p> <p style="text-align: center;"><span class="math-tex">\(\varepsilon=BLvN\)</span></p> <ul> <li><span class="math-tex">\(N\)</span> is the number of turns in the coil</li> </ul> <div class="video-embed vimeo"><iframe allow="accelerometer; 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</textarea></div><div class="modal-footer p-xs-3"><button type="button" class="btn btn-sm btn-primary btn-xs-block save-notes"><i class="fa fa-fw fa-pencil"></i>Save</button><button type="button" class="btn btn-sm btn-default btn-xs-block mx-xs-0" data-dismiss="modal" aria-label="Close">Close</button></div></div></div></div><div id="report-problem-sm-modal" class="modal fade overlay-modal report-problem" tabindex="-1" role="dialog"><div class="modal-dialog modal-sm" role="document"><div class="modal-content"><div class="modal-header p-xs-3"><h4 class="modal-title text-center my-xs-2">Report a problem for flashcard <span class="fc-viewer-id"></span></h4></div><div class="modal-body p-xs-3"><div class="msg"></div><div class="form-group mb-xs-0"><textarea class="form-control issue-description p-xs-3" rows="8"></textarea></div></div><div class="modal-footer p-xs-3"><button type="button" class="btn btn-sm btn-primary text-center btn-xs-block mb-xs-3 disabled send-report"><i class="fa fa-fw fa-paper-plane"></i>Send</button><button type="button" class="btn btn-sm btn-default text-center btn-xs-block mx-xs-0" data-dismiss="modal" aria-label="Close">Close</button></div></div></div></div> <div id="fcgame-viewer" class="modal fade modal-flashcard" tabindex="-1" role="dialog"> <div class="modal-dialog modal-lg modal-dialog-fcgame" role="document"> <div class="modal-content mc-flashcard modal-content-fcgame"> <div class="modal-header" style="background-color: #fafafa;"> <div class="row text-center" style="width: 100%;"> <div class="col-md-12"> <div style="display: flex; justify-content: space-between; align-items: center;"> <div class="text-left"> Your time: <span class="chronometer c-mobile" id="chronometer">00:00:</span> <span class="chronometer msec c-mobile" id="chronometer-msec">000</span> <br> Your best time: <span class="chronometer c-mobile" id="best-record"></span> </div> <button type="button" class="close" data-dismiss="modal" aria-label="Close"> <span 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