The figure below shows a conducting rod sliding along a pair of conducting rails

Question

The figure below shows a conducting rod sliding along a pair of conducting rails. The conducting rails have an angle of inclination of = 29.0 degrees. There is a resistor at the top of the ramp that connects the two conducting rails (R = 2.4 ohms). The mass of the rod is 0.39 kg. The rod starts from rest at the top of the ramp at time t = 0. The rails have negligible resistance and friction, and are separated by a distance L = 15.9 m. There is a constant, vertically directed magnetic field of magnitude B = 1.30 T.

1.) Find the emf induced in the rod as a function of its velocity down the rails. What is the emf when the velocity is 6.81E-3 m/s?

2.) What is the rod's terminal speed?

3.) When the rod moves at its terminal speed, what is the power dissipated in the resistor?

Explanation / Answer

a)

E=BLVcos(x) =1.2*15.9*6.81*10^-3*cos29

E=0.1136 V or 113.64 mV

b)

V=mgRTan(x)/(BL)^2cos(x)

V=0.39*9.8*2.4*tan29/(1.2*15.9)^2*cos(29)

V=0.01597m/s =0.016 m/s (approx)

c)

P=E^2/R =0.11364^2/2.5

P=5.38*10^-3 W or 5.38 mW

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

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