The conducting rod shown in the figure has length L and is being pulled along ho

Question

The conducting rod shown in the figure has length L and is being pulled along horizontal, frictionless, conducting rails at a constant velocity. The rails are connected at one end with a metal strip. A uniform magnetic field, directed out of the page, fills the region in which the rod moves. Assume that L = 13 cm, the speed of the rod is v = 7.0 m/s, and the magnitude of the magnetic field is B = 1.4 T. (a) What is the magnitude of emf induced in volts in the rod? (b) What is the current in amperes in the conducting loop? Assume that the resistance of the rod is 0.44 Ohm and that the resistance of the rails and metal strip is negligibly small, (c) At what rate is thermal energy being generated in the rod? (d) What force on the rod is needed to maintain its velocity? (e) At what rate does this force do work on the rod?

Explanation / Answer

Given that the length is L = 13 cm = 0.13 m

speed is v = 7 m/s

strength of the field is B = 1.4 T

a) the induced emf id e = BLv

                                  = 1.4 T * 0.13 m * 7 m/s

                                  = 1.27 V

b) the resistance is R = 0.44

hence the induced current is i = e/R

                                            = 1.27 V / 0.44

                                            = 2.895 A

c)     the thermal energy generated is P = i2R  

                                                          = 2.895^2 * 0.44   

= 3.7 W  

d)the force required to maintain the constant velocity is

       F = BiL

          = 1.4 T * 2.895A * 0.13 m

          =  0.527 N

e) the rate of work done by the force is

   P = Fv

       = 0.527*7

       = 3.68 W        

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