# Rod on rails in a magnetic field

• johann1301h
In summary, a rod with mass m runs on rails in a magnetic field, connected with a wire at x=0 to form a closed circuit. The total resistance in the circuit is R, and at t=0 the rod moves in positive x-direction at velocity v0. The emf in the circuit can be calculated using Lorentz's force law and Faraday's law, with the current in the circuit being dependent on time. The force on the rod is given by F=ILB, and the equation for the movement of the rod for t>0 can be derived and solved to find the position of the rod at any given time.
johann1301h

## Homework Statement

A rod with mass of m runs on rails in a magnetic field. The rails are connected with a wire at x = 0
so that the rod and the rails together with this wire form a closed circuit. The distance between the rails is L, and the resistance in the rod is R.

We assume that the rails and wire are ideal conductors, so that the total resistance in the circuit is R. At time t = 0, the rod moves in positive x-direction at velocity v0.
[/B]
https://uio-ccse.github.io/fys1120/homework/fig-week09/stav_skinner.svg
a)
Calculate the emf in the circuit using Lorentz's force law, and indicate the contribution from the different parts of the circuit.

b)
Calculate the emf with Faraday's law. Does this match the emf you calculated in the previous assignment?

c)
Find the size and direction of the current in the circuit. (With the clock)

d)
Determine the movement of the rod for t > 0. Can you check if the answer is correct using energy conservation?

2. The attempt at a solution
I believe i have solved b) and c), and a) shouldn't be to difficult, my struggle is with task d). So any help here is much appritiated!

b)
emf = BLv0

c)
I = (1/R)BLv0

d)
I think the rod wil move and then stop following a differential equation? I think the force on the rod is given by F = ILB, but the problem is that I (current) depends on the velocity of the rod! Any ideas?

The force is indeed ILB in magnitude. What is its direction? Can you write and then solve a differential equation for the motion of the rod? Its solution will tell you what the rod will do a long time after motion starts. Hint: The current is a function of time, I(t), not what you have in part (c) because the velocity v is a function of time.

I think I found the equation, see picture

#### Attachments

• Skjermbilde 2018-11-01 kl. 11.19.28.png
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johann1301h said:
I think I found the equation, see picture
That's the correct equation. Can you derive it? Do you know what to do with it?

Yes, I found v(t). see picture

#### Attachments

• Skjermbilde 2018-11-01 kl. 14.24.23.png
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johann1301h said:
Yes, I found v(t). see picture
Did you find ##v(t)## or a picture for ##v(t)##? The question is asking you to "determine the movement for t > 0" That means also finding the position of the rod ##x(t)## for t > 0. Incidentally, if you have the solution in front of you, you will be well advised to know how to reproduce it if called upon to do so on a test. By "reproduce" I don't mean "memorize", I mean "figure out the strategy for solving this kind of problem and use algebra to apply the strategy so as to get a solution." That's what learning from studying is.

## 1. What is a rod on rails in a magnetic field?

A rod on rails in a magnetic field is a common physics experiment that involves a conducting rod placed on parallel rails and subjected to a magnetic field. The rails allow the rod to move freely while the magnetic field acts as a force on the rod.

## 2. How does a rod on rails in a magnetic field work?

The movement of a rod on rails in a magnetic field is due to the Lorentz force, which is the force exerted on a charged particle by an electric and magnetic field. In this case, the magnetic field causes the electrons in the rod to experience a force perpendicular to their motion, resulting in a net force on the rod and causing it to move along the rails.

## 3. What factors affect the movement of a rod on rails in a magnetic field?

The movement of a rod on rails in a magnetic field is affected by the strength of the magnetic field, the length and orientation of the rod, and the material of the rod (conductivity and mass). Additionally, the speed and direction of the rod can also impact its movement.

## 4. What is the purpose of studying a rod on rails in a magnetic field?

Studying a rod on rails in a magnetic field allows us to understand the principles of electromagnetism and the behavior of charged particles in a magnetic field. It is also used to demonstrate the concept of electromagnetic induction and its applications in devices such as generators and motors.

## 5. How is a rod on rails in a magnetic field used in real-world applications?

A rod on rails in a magnetic field has practical applications in devices such as generators, motors, and transformers. It is also used in particle accelerators and mass spectrometers to manipulate and control charged particles. Additionally, the principles behind this experiment are essential in technologies such as magnetic levitation and magnetic resonance imaging (MRI).

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