![]() 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. 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 Example 13.4 indicates feasibility in principle. In the first, the cable hung up and could only be extended a couple of hundred meters in the second, the cable broke when almost fully extended. The ionosphere serves the same function as the stationary rails and connecting resistor in Figure 13.13, without which there would not be a complete circuit.) Drag on the current in the cable due to the magnetic force F = I ℓ B sin θ F = I ℓ B sin θ does the work that reduces the shuttle’s kinetic and potential energy, and allows it to be converted into electrical energy. (The ionosphere is the rarefied and partially ionized atmosphere at orbital altitudes. To complete the circuit, the stationary ionosphere was to supply a return path through which current could flow. This emf could be used to convert some of the shuttle’s kinetic and potential energy into electrical energy if a complete circuit could be made. The tethered satellite was to be let out on a 20-km length of wire, as shown in Figure 13.15, to create a 5-kV emf by moving at orbital speed through Earth’s field. In 19, attempts were made with the space shuttle to create large motional emfs. There is a spectacular exception, however. This small value is consistent with experience.
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