Metal bar on conducting rails

In summary, the conversation is about a problem in Griffiths Introduction to Electrodynamics involving a metal bar sliding on conducting rails with a resistor connected across them. The question asks for the current in the resistor when the bar is moving at a certain speed under the influence of a uniform magnetic field. The poster provides their attempt at a solution, which involves calculating the magnetic flux and electromotive force, but their reasoning is incorrect because it assumes constant speed. The correct solution involves considering the rate of change of flux, which accounts for the changing speed.
  • #1
natugnaro
64
1

Homework Statement



This is a Problem 7.7 fom Griffiths Introduction to Electrodynamics (3ed)

A metal bar of mass m slides frictionlessly on two parallel conducting rails a
distance l apart. A resistor R is connected across the rails and a uniform magnetic field B, pointing into page, fills the entire region.

If the bar moves to the right at speed v, what is the current in the resistor ?


Homework Equations



[tex]\Phi[/tex]=BACos[tex]\phi[/tex]
[tex]E[/tex]=[tex]\frac{d\Phi}{dt}[/tex]


The Attempt at a Solution



my reasonig is:

magnetic flux is:
[tex]\Phi[/tex]=BACos[tex]\phi[/tex]=BA=B(A0+A1).

A0 is initial surface, and A1 is surface which bar makes moving to the right with spead v.
so:

A1=x*l=v*t*l , but v is also function of t, so: A1=v(t)*t*l

I know that equation for A1 is wrong, becouse when I try to get electromotive froce
I get this:

E=d[tex]\Phi[/tex]/dt=B(0+v'(t)*t+v(t))

in solution manual it's:

E=Bl*dx/dt=Blv

Can someone explain why my reasoning is wrong, it seams logical to me.
 
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  • #2
natugnaro said:
A1=x*l=v*t*l , but v is also function of t, so: A1=v(t)*t*l
Setting x = v*t assumes that v is constant.

In any case, what matters is the rate at which flux changes, which depends on the speed at the moment in question:
d(A1) = l*v*dt
d(A1)/dt = l*v, even if v is changing.
 
Last edited:
  • #3
Ok, than you.
That will help me to answer other question from that problem.
 

1. What is a metal bar on conducting rails?

A metal bar on conducting rails is a physical setup used to demonstrate the principles of electrical conductivity. It consists of a metal bar placed on two conducting rails, with one end of the bar connected to a power source and the other end connected to a resistor.

2. How does a metal bar on conducting rails work?

The metal bar on conducting rails works by allowing an electric current to flow through the metal bar due to its high electrical conductivity. The conducting rails, which are typically made of copper, provide a low-resistance pathway for the current to flow from the power source to the resistor.

3. What factors affect the movement of the metal bar on conducting rails?

The movement of the metal bar on conducting rails is affected by several factors, including the strength of the electric current, the length and thickness of the metal bar, and the type of metal used for the bar. The presence of any magnetic fields or external forces can also affect the movement of the bar.

4. What can a metal bar on conducting rails be used to demonstrate?

A metal bar on conducting rails can be used to demonstrate the principles of electrical conductivity, Ohm's law, and the relationship between current, voltage, and resistance. It can also be used to show the effects of changing different variables, such as the length or thickness of the metal bar, on the movement of the bar.

5. Are there any safety precautions to consider when using a metal bar on conducting rails?

Yes, there are some safety precautions to consider when using a metal bar on conducting rails. It is important to ensure that the power source is not too strong to avoid overheating the metal bar. Additionally, proper insulation should be used to prevent electric shocks. It is also recommended to use gloves and safety glasses when handling the setup.

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