Consider the apparatus shown below in which a conducting bar can be moved along

Question

Consider the apparatus shown below in which a conducting bar can be moved along two rails connected to a light bulb. The whole system is immersed in a magnetic field of magnitude 8 = 0.340 T perpendicular and into the page. The distance between the horizontal rails is ( = 0.800 m. The resistance of the light bulb is R = 46.4 fl, assumed to be constant. The bar and rails have negligible resistance. The bar is moved toward the right by a constant force of F = 0.600 N. We wish to find the maximum power delivered to the light bulb. Find an expression for the current in the light bulb as a function of B, (, R, and v, the speed of the bar. When the maximum power is delivered to the light bulb, what analysis model properly describes the moving bar? Use the analysis model in part (b) to find a numerical value for the speed v of the bar when the maximum power is being delivered to the light bulb. Find the current in the light bulb when maximum power is being delivered to it. Using P = I2R, what is the maximum power delivered to the light bulb? What is the maximum mechanical input power delivered to the bar by the force F? We have assumed the resistance of the light bulb is constant. In reality, as the power delivered to the light bulb increases, the filament temperature increases and the resistance increases. Does the speed found in part (c) change if the resistance increases and all other quantities are held constant?

Explanation / Answer

so to be at constant speed

Fmagnetic = Fpull

I L B = F

B^2 L^2 v/R = F

0.34^2*0.8^2*v/46.4 = 0.6
v=376.3 m/s

d) I = B L v/R = 0.34*0.8*376.3/46.4= 2.21 A

e) P = I^2 R = 2.21^2*46.4= 225.8 W

f) P = F v = 0.6*376.3=225.8

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