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class="btn btn-default btn-block text-xs-center" data-toggle="modal" data-target="#modal-feedback" style="margin-bottom: 10px"><i class="fa fa-send"></i> Feedback</button> </div> </div> <div class="col-md-9" id="main-column"> <h1 class="page_title"> Coulombs law and field strength <a href="#" class="mark-page-favorite pull-right" data-pid="352" title="Mark as favorite" onclick="return false;"><i class="fa fa-star-o"></i></a> </h1> <ol class="breadcrumb"> <li><a href="../../../physics.html"><i class="fa fa-home"></i></a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><a href="../445/electricity-and-magnetism.html">Electricity and magnetism</a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><a href="../180/electric-fields.html">Electric fields</a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><span class="gray">Coulombs law and field strength</span></li> <span class="pull-right" style="color: #555" title="Suggested study time: 15 minutes"><i class="fa fa-clock-o"></i> 15'</span> </ol> <article id="main-article"> <p><img alt="" src="../../electricity/electromagnet.jpg" style="float: left; width: 200px; height: 133px;">Coulomb´s law is the electrical equivalent of <a href="../269/newtons-law-of-gravitation.html" title="Newton's law of gravitation">Newton's law of gravitation</a>.</p> <p>The universe is a simple place really! </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> <div class="panel panel-turquoise panel-has-colored-body panel-has-border"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Coulomb's law</p> </div> </div> <div class="panel-body"> <div> <p>The force between two point charges is proportional to the product of their charge and inversely proportional to their separation squared:</p> <h4 style="text-align: center;"><span class="math-tex">\(F \propto {Qq \over r^2}\)</span></h4> <p>NB: Force is measured in Newtons.</p> <p>You don't need to go inside spheres of charge for the IB (we can assume that all of the charge acts at the centre)... but in your spare time you can go where you like.</p> <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/172726092"></iframe></div> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-turquoise panel-has-colored-body panel-has-border panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Field strength</p> </div> </div> <div class="panel-body"> <div> <p>Electric field strength is the force experienced per unit charge by a small positive charge:</p> <h4 style="text-align: center;"><span class="math-tex">\(E= {F\over q}\)</span></h4> <p>NB: Field strength is measured in N C<sup>-1</sup>.</p> <p>When defining field strength, don't forget that the test charge is positive.</p> <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/172964120"></iframe></div> </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-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> <p>A sphere of charge acts like all the charge was at its centre. Inside the sphere the charge is zero.</p> <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/172942337"></iframe></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 quizzes to practise application of theory.</em></p> <br><a class="btn btn-primary btn-block text-center" data-toggle="modal" href="#338bb2a3"><i class="fa fa-play"></i> START QUIZ!</a><div class="modal fade modal-slide-quiz" id="338bb2a3"> <div class="modal-dialog" style="width: 95vw; max-width: 960px"> <div class="modal-content"> <div class="modal-header slide-quiz-title"> <h4 class="modal-title" style="width: 100%;"> Coulombs law and field strength <strong class="q-number pull-right"> <span class="counter">1</span>/<span class="total">1</span> </strong> </h4> </div> <div class="modal-body p-xs-3"> <div class="slide-quiz" data-stats="6-95-352" style="opacity: 0"> <div class="exercise shadow-bottom"><div class="q-question">The force between 2 charged bodies is F. What is the force if the charge on one of the bodies is doubled?</div><div class="q-answer"><p><label class="radio"><input type="radio"> F</label></p><p><label class="radio"><input type="radio"> 3F</label></p><p><label class="radio"><input class="c" type="radio"> 2F</label></p><p><label class="radio"><input type="radio"> 4F</label></p></div><div class="q-explanation"><p>F = kQ<sub>1</sub>Q<sub>2</sub>/r<sup>2</sup><br>k2Q<sub>1</sub>Q<sub>2</sub>/r<sup>2</sup> = 2F</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The force between 2 charged spheres is F. What is the force if their separation is reduced by a factor 4</p></div><div class="q-answer"><p><label class="radio"><input class="c" type="radio"> 16F</label></p><p><label class="radio"><input type="radio"> F/16</label></p><p><label class="radio"><input type="radio"> 4F</label></p><p><label class="radio"><input type="radio"> F/4</label></p></div><div class="q-explanation"><p>F <span class="st">∝ 1/r<sup>2 </sup></span></p><p>1/(r/4)<sup>2</sup> = 16/r<sup>2</sup></p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The diagram shows two sphere of charge. The force experienced by sphere A is F.</p><p style="text-align: center;"><img alt="" src="../../efieldq3.jpg" style="width: 199px; height: 82px;"></p><p>The next diagram shows the same bodies but arranged differently</p><p style="text-align: center;"><img alt="" src="../../efieldq3a.jpg" style="width: 188px; height: 85px;"></p><p>The force on A is now</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> F/16</label></p><p><label class="radio"><input type="radio"> F/8</label></p><p><label class="radio"><input type="radio"> F/4</label></p><p><label class="radio"><input class="c" type="radio"> F/2</label></p></div><div class="q-explanation"><p>F = 4Q x 4Q/r<sup>2</sup></p><p>F´=4Q x 2Q /r<sup>2</sup></p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The diagram shows two sphere of charge. The force experienced by sphere A is F.</p><p style="text-align: center;"><img alt="" src="../../efieldq3.jpg" style="width: 199px; height: 82px;"></p><p>The next diagram shows the same bodies but arranged differently</p><p style="text-align: center;"><img alt="" src="../../efield4a.jpg" style="width: 205px; height: 84px;"></p><p>The force is now</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> 0</label></p><p><label class="radio"><input type="radio"> F/2</label></p><p><label class="radio"><input type="radio"> -F/8</label></p><p><label class="radio"><input class="c" type="radio"> -F/4</label></p></div><div class="q-explanation"><p>F = 4Q x 4Q/r<sup>2</sup></p><p>F´=2Q x -2Q /r<sup>2</sup></p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The diagram shows two sphere of charge. The force experienced by sphere A is F.</p><p style="text-align: center;"><img alt="" src="../../efieldq3.jpg" style="width: 199px; height: 82px;"></p><p>The next diagram shows the same bodies but arranged differently</p><p style="text-align: center;"><img alt="" src="../../efieldq5a.jpg" style="width: 331px; height: 118px;"></p></div><div class="q-answer"><p><label class="radio"><input type="radio"> F/4</label></p><p><label class="radio"><input class="c" type="radio"> F/8</label></p><p><label class="radio"><input type="radio"> F/16</label></p><p><label class="radio"><input type="radio"> F/2</label></p></div><div class="q-explanation"><p>F = 4Q x 4Q/r<sup>2</sup></p><p>F´=2Q x 4Q /(2r)<sup>2</sup></p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The unit of field strength is</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> C<sup>2</sup>m<sup>-1</sup></label></p><p><label class="radio"><input class="c" type="radio"> NC<sup>-1</sup></label></p><p><label class="radio"><input type="radio"> C<sup>2</sup>m<sup>-2</sup></label></p><p><label class="radio"><input type="radio"> CN<sup>-1</sup></label></p></div><div class="q-explanation"><p>E is force per unit charge</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The field strength at a point is 1000 NC<sup>-1</sup></p><p>The force experienced by a 1 μC charge placed at that point is:</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> 1 N</label></p><p><label class="radio"><input type="radio"> 1 nN</label></p><p><label class="radio"><input class="c" type="radio"> 1 mN</label></p><p><label class="radio"><input type="radio"> 1 kN</label></p></div><div class="q-explanation"><p>1000 x 1 x 10<sup>-6 </sup>= 1 x 10<sup>-3</sup></p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The diagram represents two points in an electric field</p><p style="text-align: center;"><img alt="" src="../../efieldq8(1).jpg" style="width: 270px; height: 281px;"></p><p>If the field at A has magnitude E, the field at B ill have magnitude:</p></div><div class="q-answer"><p><label class="radio"><input class="c" type="radio"> E/4</label></p><p><label class="radio"><input type="radio"> 1 E</label></p><p><label class="radio"><input type="radio"> E/8</label></p><p><label class="radio"><input type="radio"> E/2</label></p></div><div class="q-explanation"><p>The field is radial so</p><p>E is inversely proportional to distance from centre</p><p>Twice the distance from the centre so 1/4 the field</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The diagram represents two points in an electric field</p><p style="text-align: center;"><img alt="" src="../../efieldq8a.jpg" style="width: 138px; height: 173px;"></p><p>If the field at A is E the field at B is:</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> 2E</label></p><p><label class="radio"><input class="c" type="radio"> 1E</label></p><p><label class="radio"><input type="radio"> E/4</label></p><p><label class="radio"><input type="radio"> E/2</label></p></div><div class="q-explanation"><p>Uniform field is the same everywhere</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The diagram represents two points in an electric field</p><p style="text-align: center;"><img alt="" src="../../afieldq9a.jpg"></p><p>If the field at A is E the field at B is:</p></div><div class="q-answer"><p><label class="radio"><input class="c" type="radio"> E/2</label></p><p><label class="radio"><input type="radio"> 2E</label></p><p><label class="radio"><input type="radio"> E/4</label></p><p><label class="radio"><input type="radio"> 1E</label></p></div><div class="q-explanation"><p>Field strength is proportional to line density.</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The diagram represents two charges.</p><p style="text-align: center;"><img alt="" src="../../efield10a.jpg" style="width: 422px; height: 195px;"></p><p>Which arrow gives the resultant field at the point shown?</p></div><div class="q-answer"><p><label class="radio" style=" float: left; margin-right: 40px; "><input class="c" type="radio"> D</label></p><p><label class="radio" style=" float: left; margin-right: 40px; "><input type="radio"> A</label></p><p><label class="radio" style=" float: left; margin-right: 40px; "><input type="radio"> B</label></p><p><label class="radio" style=" float: left; margin-right: 40px; "><input type="radio"> C</label></p></div><div class="q-explanation"><p style="text-align: center;"><img alt="" src="../../efielda10a.jpg" style="width: 422px; height: 195px;"></p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The diagram represents 2 charges</p><p style="text-align: center;"><img alt="" src="../../efield11a.jpg" style="width: 422px; height: 207px;"></p><p>Which arrow gives the resultant field at the point shown?</p></div><div class="q-answer"><p><label class="radio" style=" float: left; margin-right: 40px; "><input class="c" type="radio"> A</label></p><p><label class="radio" style=" float: left; margin-right: 40px; "><input type="radio"> B</label></p><p><label class="radio" style=" float: left; margin-right: 40px; "><input type="radio"> C</label></p><p><label class="radio" style=" float: left; margin-right: 40px; "><input type="radio"> D</label></p></div><div class="q-explanation"><p style="text-align: center;"><img alt="" src="../../efielda11a.jpg" style="width: 422px; height: 207px;"></p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The diagram represents 2 charges</p><p style="text-align: center;"><img alt="" src="../../efieldq12.jpg"></p><p>The red arrow shows the fiekd due to the positive charge.</p><p>Which arrow represents the resultant?</p></div><div class="q-answer"><p><label class="radio" style=" float: left; margin-right: 40px; "><input class="c" type="radio"> B</label></p><p><label class="radio" style=" float: left; margin-right: 40px; "><input type="radio"> A</label></p><p><label class="radio" style=" float: left; margin-right: 40px; "><input type="radio"> C</label></p><p><label class="radio" style=" float: left; margin-right: 40px; "><input type="radio"> D</label></p></div><div class="q-explanation"><p>E is proportional to Q/r<sup>2</sup> so the field due to the negative charge is 2x the field due to the positive</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The diagram represents a positive test charge in a hollow sphere.</p><p style="text-align: center;"><img alt="" src="../../efieldq20.jpg" style="width: 210px; height: 191px;"></p><p>The direction of the force experienced by the test charge is:</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> right</label></p><p><label class="radio"><input type="radio"> out of the page</label></p><p><label class="radio"><input class="c" type="radio"> There is no force</label></p><p><label class="radio"><input type="radio"> left</label></p></div><div class="q-explanation"><p>The field inside a hollow sphere of charge is zero</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The diagram represents 4 charges placed on the corners of a square and a test charge.</p><p style="text-align: center;"><img alt="" src="../../efieldq21.jpg" style="width: 254px; height: 235px;"></p><p>The direction of force experienced by the test charge is:</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> left</label></p><p><label class="radio"><input class="c" type="radio"> right</label></p><p><label class="radio"><input type="radio"> out of the page</label></p><p><label class="radio"><input type="radio"> there is no force</label></p></div><div class="q-explanation"><p>Vertical components cancel but the test charge is closer to the charges on the left so the force right will be greater.</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The field inside a hollow metal sphere of charge is zero because:</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> there is no charge inside the sphere</label></p><p><label class="radio"><input class="c" type="radio"> the vector sum of the force due to each charge is zero</label></p><p><label class="radio"><input type="radio"> the potential energy of charges inside the sphere is zero</label></p><p><label class="radio"><input type="radio"> there is no metal inside the sphere</label></p></div><div class="q-explanation"></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div> </div> </div> <div class="modal-footer slide-quiz-actions"> <div class=""> <div class="pull-left pull-xs-none mb-xs-3"> <button class="btn btn-default d-xs-none btn-prev"> <i class="fa fa-arrow-left"></i> Prev </button> </div> <div class="pull-right pull-xs-none"> <button class="btn btn-success btn-xs-block text-xs-center btn-results" style="display: none"> <i class="fa 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