Rod on Rails Two The conducting rod shown in Fig. 31-42 has a length L and is be

Question

Rod on Rails Two The conducting rod shown in Fig. 31-42 has a length L and is being pulled along horizontal, frictionless, conducting rails at a constant velocity v. 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 = 17 cm, v = 6.4 m/s, and B = 1.0 T.

Figure 31-42
(a) What is the magnitude of the emf induced in the rod?
V
(b) What is the magnitude and direction of the current in the conducting loop? Assume that the resistance of the rod is 0.40 and that the resistance of the rails and metal strip is negligibly small.
A
(c) At what rate is thermal energy added to the rod?
W
(d) What magnitude of force must be applied to the rod by an external agent to maintain its motion?
N
(e) At what rate does this external agent do work on the rod?
W Compare the answer for (e) with the answer to (c).


Section 31.6 Induction and Energy Transfers


DIAGRAM

http://img809.imageshack.us/i/3154.gif/

Explanation / Answer

Given Length of the conducting rod, L = 0.17 m Magnetic field , B = 1.0 T Speed , v = 6.4 m/s a) Magnitude of induced emf in the rod is     = d / d t where flux = BA = B L v t      d / d t = BLv = BLv = 1.0 T * 0.17 m *6.4 m/s = 1.088 V b) Resistance of the rod, R = 0.40     Current in the loop , I = / R = 1.088 V / 0.40      I = 2.72 A Direction of current is clock wise c) Rate at which thermal energy is added is     Rate of thermal energy = I^2 R = (2.72 A)^2 * 0.40                                        = 2.95 W d) Magnitude of Force is, F = I BL = 2.72 A * 1.0 T *0.17 m                                        F = 0.46 N e) Rate of work is , F v =0.46N * 6.4 m/s = 2.95 W    This result is equal to the rate of thermal energy added    

Related Questions

Navigate

• Browse (All)
• Browse R
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.