Exploring Problem 7.7: Frictionless Metal Bar on Conducting Rails

[mathnerd15]

I'm not taking this course for credit...

Hi! Is this a good text after Halliday?
I'm trying problem 7.7-
a metal bar of mass m slides frictionlessly on 2 conducting rails...
perhaps the current is I=integral J dot da, generated by the moving metal bar, velocity v (results in changing reference frame and B field which results in EMF driving current vertically up through the wire?) is the force diagram similar to 7.11?
I'm unclear on the geometry of the force digram?

thanks very much

 

[mathnerd15]

I'm curious at what point does a great physicist have the intuition for these problems- is it something that you are born with?

 

[MisterX]

Do you know how to find the magnetic force on a stationary wire that is carrying current?
I wouldn't think about current density in a problem like this; it is intuitive to me that the total current through the bar is what matters for the force, regardless of the cross sectional distribution of current density.

 

[mathnerd15]

Biot-Savart law

thanks very much!
Isn't that the beautiful Biot-Savart law where muo is the permeability of free space? uo=4pi*10^-7N/A^2)
(muo/4pi)Integral[ (I X r )dl'/r^2 ]

there is the interesting situation of the Infinite Wire- theta1=-pi/2, theta2=pi/2B= muoI/(2pi s)
and as you know there is a form for surface and volume currents
I'm just starting to look at these...

 

[paranormal]

for the question! I am always happy to discuss and explore interesting problems like this one.

First of all, it's great that you are tackling problem 7.7 and thinking about the application of concepts from Halliday's text. This problem involves a metal bar sliding on conducting rails, which is a classic example of electromagnetic induction. In this case, the movement of the metal bar generates a changing magnetic flux, which in turn induces an electromotive force (EMF) and drives a current through the wire.

To understand the force diagram, it may be helpful to consider the geometry of the problem. The metal bar is sliding on two conducting rails, which are connected at one end to a battery. This creates a closed loop circuit, with the metal bar acting as a moving conductor. As the metal bar slides, it experiences a Lorentz force due to the interaction between the magnetic field and the current flowing through the wire.

The force diagram for this problem would be similar to problem 7.11, which also involves a moving conductor in a magnetic field. However, in this case, the force acting on the metal bar would be perpendicular to both the direction of motion and the magnetic field. This can be determined using the right-hand rule, where the thumb points in the direction of motion and the fingers point in the direction of the magnetic field, resulting in a force perpendicular to both.

I hope this helps clarify the problem and the force diagram for you. Keep exploring and asking questions, that's what science is all about!