Correct answer 1 While a rectangular wire loop is pulled upward through a uniform magnetic eld B eld penetrating its bottom half as shown there is a current in the loop Week 9 Day 1 Concept Question Loop in Uniform Field Faraday s Law of Induction Changing magnetic ux induces a current Magnetic Flux Through Wire Loop Flux is the Generalization of Flow Uniform magnetic eld Non Uniform Magnetic Field Electromotive Force Product of perpendicular component of magnetic eld and area Imagine a charge q moving around a closed path under the action of a force F Then the work done per unit charge is called the electromotive force Has the same dimensions as the electric potential so SI unit is the volt If the closed path is a circuit with resistance R then the electromotive force will cause a current to ow according to Correct answer 3 While a rectangular wire loop is pulled sideways through a uniform magnetic eld B eld penetrating its bottom half as shown there is no current in the loop Motional emf Pull a loop with speed v through a uniform magnetic eld At one instant time electromotive force is Concept Question Loop In Uniform Field Ways to Induce emf Quantities which can vary with time Magnitude of B Area enclosed by the loop Angle between B and normal vector loop Group Problem Changing area Conducting rod pulled along two conducting rails in a uniform magnetic eld B at constant velocity v Calculate the magnitude of the derivative of the magnetic ux with respect to time Calculate the magnitude of EMF due to the magnetic force Does your result agree with your result from part a What is the magnitude of induced current Generalization Faraday s Law Loop is at rest and magnet is moving resulting in a changing magnetic ux through the loop and an induced emf and current in the loop Induced Electric Field and Electromotive Force emf An induced electric eld appears in the current loop resulting in an electric force on the charges in the conductor producing an induced current Faraday s Law of Induction Sign Conventions Right Hand Rule If C is a stationary closed curve and S is a surface spanning C then The changing magnetic ux through S induces a non electrostatic electric eld whose line integral around C is non zero By the right hand rule RHR clockwise integration direction for line integral of electric eld emf requires that unit normal points into plane of gure for magnetic ux surface integral Magnetic ux positive into page negative out of page By the right hand rule RHR counterclockwise integration direction for line integral of electric eld emf requires that unit normal points out of plane of gure for magnetic ux surface integral Magnetic ux positive out of page negative into page Group Problem Induced Electric Field Consider a uniform magnetic eld which points into the page and is con ned to a circular region with radius R Suppose the magnitude increases with time i e dB dt 0 Find the magnitude and direction of the electric eld in the regions i r R ii r R iii Plot the magnitude of the electric eld as a function r Lenz s Law Direction of Induced Current Induced EMF is in the direction that opposes the change in ux that caused it For a Closed Conduction Path Direction of Induced Current Induced current is source of induced magnetic ux that opposes the change in magnetic ux that caused it For a counterclockwise integration direction for the line integral hence a upwards unit normal for the surface integral Concept Question Loop Correct answer 1 The magnetic eld through a wire loop is pointed upwards and increasing with time The induced current in the coil is clockwise Concept Question Moving Loop Correct answer 1 A circuit in the form of a rectangular piece of wire is pulled away from a long wire carrying current I in the direction shown in the sketch The induced current in the rectangular circuit is clockwise Concept Question Faraday s Law Loop Correct answer 4 A coil moves up from underneath a magnet with its north pole pointing upward The current in the coil is counterclockwise and the force on the coil is down Conclusion Faraday s Law of Induction Changing magnetic ux generates electromotive force that opposes that change in ux STOPPED HERE IN CLASS
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