AA = (AX Ах (a) O increasing RHR-2 в Application of Lenz's law RHR-1 R #E Equivalent circuit (b) Figure 23.11 (a) A motional emf = Btv is induced between the rails when this rod moves to the right in the uniform magnetic field. The magnetic field B is into the page, perpendiculer to the moving rod and rails and, hence, to the area enclosed by them. (b) Lenz's law gives the directions of the induced field and current, and the polarity of the induced emf. Since the flux is increasing, the induced field is in the opposite direction, or out of the page. RHR-2 gives the current direction shown, and the polarity of the rod will drive such a current. RHR-1 also indicates the same polarity for the rod. (Note that the script E symbol used in the equivalent circuit at the bottom of part (b) represents emf.)
AA = (AX Ах (a) O increasing RHR-2 в Application of Lenz's law RHR-1 R #E Equivalent circuit (b) Figure 23.11 (a) A motional emf = Btv is induced between the rails when this rod moves to the right in the uniform magnetic field. The magnetic field B is into the page, perpendiculer to the moving rod and rails and, hence, to the area enclosed by them. (b) Lenz's law gives the directions of the induced field and current, and the polarity of the induced emf. Since the flux is increasing, the induced field is in the opposite direction, or out of the page. RHR-2 gives the current direction shown, and the polarity of the rod will drive such a current. RHR-1 also indicates the same polarity for the rod. (Note that the script E symbol used in the equivalent circuit at the bottom of part (b) represents emf.)
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Question
Derive an expression for the current in a system like shown, under the following conditions. The resistance between the rails is R , the rails and the moving rod are identical in cross section A and have the same resistivity ρ .
The distance between the rails is l, and the rod moves at constant speed v perpendicular to the uniform field B . At time zero, the moving rod is next to the resistance R .
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