標題:
an e.m question
發問:
1. A conductor XY of mss m slides from rest down a pair of frictionless rails which are separted by a distance r and inclined at an angle A to the horizontal. A uniform magnetic field of flux density B acts vertically upwards. Deduce an equation for the e.m.f. induced in the conductor XY in terms of B, r, A, g and... 顯示更多 1. A conductor XY of mss m slides from rest down a pair of frictionless rails which are separted by a distance r and inclined at an angle A to the horizontal. A uniform magnetic field of flux density B acts vertically upwards. Deduce an equation for the e.m.f. induced in the conductor XY in terms of B, r, A, g and s, where s is the displacement of the conductor rom its rest position and g is the acceleration of gravity. 更新: a = g.sin(A), why?
最佳解答:
One more parameter is required: The resistance of the conductor XY. Also, suppose that the rails are perfectly conducting, then with reference to the diagrams below: 圖片參考：http://i388.photobucket.com/albums/oo325/loyitak1990/Sep10/CrazyEM2.jpg Note: It is rather to relate the induced e.m.f. with the displacement s since to find s, we have to integrate v w.r.t. time t first. Afterwards, for certain value of s, we need to evaluate for t which is rather complicated and then we need to sub it back to the expression of v.
其他解答:
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Induced emf E of a moving conductor in a magentic field is given by, E = B.r.v where v is the velocity of the conductor. Since the conductor starts from rest, use equation of motion: v^2 = u^2 + 2.a.s with u = 0 m/s, a = g.sin(A), hence, v^2 = 2.g.s.sin(A) Therefore, E = B.r.square-root[2gs.sin(A)]
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