![]() " The induced emf around a closed mathematical path in magnetic field is equalto the rate of change of the magnetic flux intercepted by the area within thepath " If we consider a closed path, Faraday's law can be stated as follows: " The induced emf along a moving or changing mathematical path in a constant orchanging magnetic field equals the rate at which magnetic flux sweeps acrossthe path. The relation between the induced emf andthe change in magnetic flux is known as Faraday's law of induction: In both casesthe result will be an induced emf. The enclosed magnetic flux can also bechanged if the strength of the enclosed magnetic field changes. In the system shown in Figure 32.1 the enclosed fluxchanges due to the motion of the rod. It holds for rods and wires of arbitrary shape movingthrough arbitrary magnetic fields.Įquation (32.5) relates the induced emf to the rate at which the enclosedmagnetic flux changes. ThusĪlthough this formula was derived for the special case shown in Figure 32.1, itis valid in general. The quantity BvL is the magnetic flux swept across by the rod persecond. Lookingat Figure 32.1 we observe that vL is the area swept across by the rod persecond. Equation (32.4)shows that the magnitude of the emf is proportional to the velocity v. Since the emf is associated with the motion of the rod throughthe magnetic field it is called motional emf. If the ends of the rod are connected with acircuit providing a return path for the accumulated charge, the rod will be asource of emf. The induced electric field will generate a potential difference Vbetween the ends of the rod, equal to As this point the upward flow of electrons will stop and The strength of this electric field will increase until theelectrostatic force produced by this field is equal in magnitude to themagnetic force. This charge distribution will produce an electric field inthe rod. ![]() The charge distribution of the rod willtherefore change, and the top of the rod will have an excess of electrons(negative charge) while the bottom of the rod will have a deficit of electrons(positive charge). Moving conductor in magnetic field.Īs a result of the magnetic force electrons will start toaccumulate at the top of the rod. The magnetic force acting on a freeelectron in the rod will be directed upwards and has a magnitude equal toįigure 32.1. Figure 32.1 shows a rod, made of conducting material, being moved with avelocity v in a uniform magnetic field B. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License. We recommend using aĪuthors: Paul Peter Urone, Roger Hinrichs Use the information below to generate a citation. Then you must include on every digital page view the following attribution: If you are redistributing all or part of this book in a digital format, Then you must include on every physical page the following attribution: If you are redistributing all or part of this book in a print format, Want to cite, share, or modify this book? This book uses the The current is a result of an emf induced by a changing magnetic field, whether or not there is a path for current to flow. More basic than the current that flows is the emf that causes it. ![]() It is the change in magnetic field that creates the current. Closing and opening the switch induces the current. Interestingly, if the switch remains closed or open for any length of time, there is no current through the galvanometer. ![]() (You can also observe this in a physics lab.) Each time the switch is opened, the galvanometer detects a current in the opposite direction. It was found that each time the switch is closed, the galvanometer detects a current in one direction in the coil on the bottom. The galvanometer is used to detect any current induced in the coil on the bottom. When the switch is closed, a magnetic field is produced in the coil on the top part of the iron ring and transmitted to the coil on the bottom part of the ring. The apparatus used by Faraday to demonstrate that magnetic fields can create currents is illustrated in Figure 23.3.
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