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# Example 6-3: Sliding BarThe rectangular loop shown in Fig. 6-8 has a constant width l,but its length x0 increases with time as a conducting bar slideswith uniform velocity u in a static magnetic field B = zˆB0x.Note that B increases linearly with x. The bar starts from x = 0at t = 0. Find the motional emf between terminals 1 and 2 andthe current I flowing through the resistor R. Assume that theloop resistance Ri % R.Solution: This problem can be solved by using the motionalemf expression given by Eq. (6.26) or by applying the generalformula of Faraday’s law. We now show that the two approachesyield the same result.The sliding bar, being the only part of the circuit that crossesthe lines of the field B, is the only part of contour 2341 thatcontributes to V memf. Hence, at x = x0, for example,V memf = V12 = V43 =#43(u × B)· dl =#43(xˆu × zˆB0x0)· yˆ dl= −uB0x0l.The length of the loop is related to u by x0 = ut. Hence,V memf = −B0u2lt (V).

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