5) A bar of length l = 15.0 cm and mass m = 0.180 kg, having a resistance of R =

Question

5) A bar of length l = 15.0 cm and mass m = 0.180 kg, having a resistance of R = 150 ohms, is free to slide on two vertical, conducting rods, as shown in Fig. 3a. There is a uniform magnetic field of magnitude B = 1.08 T directed out of the paper in the yellow-shaded region. An emf of E = 3,000 V is placed across the bar. The bar is then pushed down a distance d = 7.50 cm into the region with the magnetic field, as shown in Fig. 3b. a) What is the highest height the bar will reach after it is let go? (Ignore the emf that is generated by the motion of the bar in the magnetic field.) b) After the bar is let go, what is the emf generated by the motion of the bar just before it reaches y = 0? c) If the bar ever gets above y = 0, what would the generated emf be in the region above y = 0? d) Discuss as completely as you can, how the generated emf will affect the motion of the bar. e) Will the effect of the generated emf on the motion of the bar be greater or less if the bar is pushed down more than 7.50 cm before it is let go?

Explanation / Answer

emf = Blv
where B = magnetic field = 1.08T
l = length of rod = 0.15m

v = velocity of rod

3 = 1.08*0.15*v

v = 18.52 m/s

highest point,

1/2*0.180*v^2 = mgh

h = 17.50 m

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