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Faraday's Law: Building An Electric Motor OBJECTIVE: To build and operate an electric motor and in the process understand the underlying physical concept involved – Faraday's Law. EQUIPMENT: ScienceFirst™ DC Motor Kit (INSULATORS: plastic base, commutators, commutator insulators, shaft supports; CONDUCTORS: coated copper wire, metal shaft, field pole, mounting bracket, armature halves, wire brushes, fasteners, battery clips. See the illustrated parts list later in this write-up. INTRODUCTION: Faraday's Law - Theory Two weeks ago, you saw how a permanent magnet exerted a force on a current-carrying wire (and vice versa). In that lab, the positions of the wire and magnet were unchanged and the current was constant (except when you varied it to see how the force changed). So both magnetic fields were unchanged, resulting in a constant force between wire and magnet. In this lab, we will examine the consequences and applications of wires and magnets in the presence of a changing magnetic field. The field can be changed either by varying the strength of a magnet (as in decreasing the current in an electromagnet) or varying the relative position of a magnet (as in moving towards a permanent magnet). Numerous inventions, such as the telephone, electric generators, electric guitar pickups, electrical transformers, car cruise controls, induction stoves and blood flow meters – and of course electric motors - all exploit the fact that a changing magnetic field can give rise to an electrical current, a phenomenon we call electromagnetic induction. The mathematical law that relates the changing magnetic field to the induced current (or, more accurately, the induced voltage or emf) is called Faraday's Law, named after the man (among others) who first observed it in the laboratory around 1830. You may recall from lecture that magnetic flux through a surface in a magnetic field B is = ∫ B. n dA where n is a unit vector perpendicular to area element dA note that if B is constant and the surface is a plane with area A, this reduces to =B Acos A conducting loop which has an ammeter attached to it will register a current if the magnetic flux through the loop changes in time. The change may arise from motion: Or the change in flux may be due to the changing current in a circuit. In (a) below there is no induced emf in loop 2 but when the battery is connected, the increasing current in loop 1 produces a changing magnetic field and hence induces an emf in loop 2. Faraday noted that the emf induced in a loop is proportional to the rate of change of magnetic flux though it: d dt where is the electromotive force induced (measured in volts) and N is the number of turns of the coil. Provided each turn of the coil is sized and oriented like the others, its contribution is simply additive; hence the coefficient N in front of the flux derivative. =−N Notice the negative sign. Lenz's Law states that the induced emf (and current) will be in a direction such that the induced magnetic field opposes the original magnetic flux change. Keep in mind that the induced current will now produce an induced magnetic field. The direction of that magnetic field will be opposite to the direction the flux is changing. When we are moving a magnet around a coil, we are inducing a current in it. In order to do this we have performed work on the magnet because we had to oppose a force to keep the magnet moving, even at constant velocity. What is the source of this force? According to Lenz's Law, the induced current produces an induced magnetic field, which is represented by a magnetic moment (denoted by m on the diagram below, which opposes the motion of the magnet. This magnetic moment can be thought of as "virtual magnet" whose poles either oppose or attract the real magnet, depending on the direction of motion. In either case, the direction of induced current can be identified using your right hand: point your extended thumb in the North direction of the magnetic moment; your fingers will curl in the direction the current is going through the loop. Doing work on a magnet to create a current is the basis behind an electrical generator. In hydroelectric dams, falling water turns large paddles connected to electrical generators that convert mechanical energy to electrical energy. Conversely, we can use changing flux to do work. This is the principle behind an electric motor. Electric Motor An electric motor converts electrical energy to mechanical energy. The main idea is to have two magnets of opposite polarity continually pushing against each other to turn a shaft: In the illustration above, the motor's shaft is perpendicular to the plane of the paper. A fixed electromagnet is at the bottom, while a rotating electromagnet (also called the armature) is affixed to the shaft above the bottom one. Both electromagnetic coils form a continuous current loop and share the same electrical power supply (DC power supply or battery). The armature is connected directly to the battery and its winding terminates in the two vertical brushes. The rotating electromagnet (see side-diagonal view below) gets its electricity from the commutator wires which are at the ends of its winding. You may notice that the wires touch the brushes only part of the time – around the time when the armature is approximately vertical. It is very important to note that when the armature has rotated 180 degrees from its initial vertical orientation, the armature current (and hence the magnetic field) reverses direction. This is like swapping the “+” and “-” cables out of the power supply every rotation. In this fashion the two electromagnets are always repelling each other. Of course it is quite possible for the armature to settle into the equilibrium position – the horizontal position – but if the armature is already rotating, its angular momentum will perpetuate the constant repulsion impulses as it passes both vertical positions. This is why it is often necessary to give the motor a spin to get it started. Procedure NOTE: The instructions call for a battery to be used but in this lab we will use a power supply, which you are already familiar with. See motor.pdf, the other file on this webpage or folder, which has a comprehensive illustrated parts list and detailed instructions on how to assemble the motor. Also see the section on troubleshooting if you cannot get your motor to run. Here are some key points to check: - Initially set the power supply meter to AMPS (instead of VOLTS). To duplicate a typical battery voltage, use an voltage no higher than 1.5V when the motor is spinning. You may need a higher voltage to get the motor started – do not exceed 1.7V. If you notice that the power supply is continually clicking with the CC and CV indicator lights (LEDs) alternately flashing, it is trying to limit the current; in that case raise that threshold by raising the Current (turn the knobs clockwise) – then you should be able to adjust the Voltage properly. - It is vital to scrape off the insulation from the coil ends. Remove any kinks, straighten out bends, and scrape off (in one direction, toward the end of the wire) with sandpaper. - The instructions call for the holes in the commutator to be perpendicular to the armature – you may have to adjust this up to several degrees in either direction. - To make sure there is a complete electrical loop, raise the power supply to 1.5V, set the meter to AMPS and rotate the armature such that the commutator wires touch the brushes – if both electromagnets are getting power, there will be a current reading. ***Do not answer the questions in the instructions – enter the answers to the questions given below in the Hand-in Sheet.*** Questions 1. Assuming that current leaves the power supply's (+) terminal and enters its (-) terminal, draw the direction of the magnetic fields (indicate with vector arrows) in both armature and fixed (bottom) coils when the armature is vertical (in contact with the brushes). 2. Draw the direction of the magnetic fields (indicate with vector arrows) in both armature and fixed (bottom) coils when the armature is horizontal (NOT in contact with the brushes). 3. Draw the direction of the magnetic fields (indicate with vector arrows) in both armature and fixed (bottom) coils when the armature is again vertical (once again in contact with the brushes, but this time 180 degrees from its position in Question 1). 4. Answer this before you actually do this little experiment – does the direction of motor spin change if you switch the (+) and (-) terminals on the power supply? Do the experiment – is your answer confirmed? Explain. 6. In page 5 of this write-up, it is mentioned that the equilibrium position is when the armature is horizontal – why does it prefer to settle into this position? 7. Without exceeding 1.5V, can you determine if there is a relationship between the angular speed of the motor and the Voltage? 8. You have built a DC (direct current) motor. Would it still run if you connected it to an AC (alternating current, like the one that comes out of your wall outlet in hour house or dorm) power supply? Explain why or why not.