Mechanics or what?

Electricity and Magnetism Level 2

A horizontal conducting rod of mass m m is free to slide on two vertical conducting rails as shown. What is the terminal speed of the rod?

Details and Assumptions:

  • A uniform magnetic field of intensity B B exists throughout the region and points into the screen.
  • The length of the rod is L L .
  • The resistor has resistance R R .

Bonus What will happen if the magnetic field is outward? Will the rod attain terminal velocity?

Try my next problem here

m g L B R \dfrac{mgL}{BR} B 2 L 2 m g R \dfrac{B^2L^2}{mgR} m g R B 2 L 2 \dfrac{mgR}{B^2L^2} m g R B L \dfrac{mgR}{BL}

Sparsh Sarode by Sparsh Sarode , 22, India

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1 solution

Sparsh Sarode
Jun 23, 2016

At terminal velocity, induced EMF, e = B v L e=BvL where v is the terminal velocity of the rod

i = e R i=\dfrac{e}{R}

i = B v L R i=\dfrac{BvL}{R}

Upwards force experienced by rod is

F B = B i L F_B=BiL

F B = B 2 L 2 v R F_B=\dfrac{B^2L^2v}{R}

This should be equal to m g mg

∴ v = m g R B 2 L 2 \therefore v=\dfrac{mgR}{B^2L^2}

6 Helpful 0 Interesting 0 Brilliant 0 Confused

Not as easy as it looks!!!

Rishi K - 4 years, 11 months ago

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Yep. What about the bonus question?

Sparsh Sarode - 4 years, 11 months ago

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Thats brilliant too...:p

Rishi K - 4 years, 11 months ago

Actually, if you look really closely at the options, dimensional homogeneity can be used, though that method is a little bland. This answer is much more satisfying!

B.S.Bharath Sai Guhan - 4 years, 11 months ago

I also did this by dimensional method . Its quite easy.but this is a more vivid soln.

Sargam yadav - 4 years, 11 months ago

is there a good wiki to look at for this?

Matthew Agona - 4 years, 6 months ago

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