Electrodynamics (Lorentz to Faraday)

In summary, you pull a straight wire through a magnetic field. The Lorentz force causes charges on the wire to move with a velocity opposite to the direction of the wire.
  • #1
iScience
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Electrodynamics (Lorentz Force & Voltage) [edited]

Two part inquiry


PART I


Situation: I have a B-field and I'm pulling a straight piece of wire through that B-field


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You pull the wire perpendicularly through the B-field at velocity v; charges between points a and b will experience the Lorentz Force and will begin to move along the wire with velocity u, and thus will experience a force opposite to the direction which you are pulling the wire.



Goal: Trying to derive the work done on a unit charge the classical way (by integrating along the path it takes)


Let us define the force per unit q to pull the wire through the field: f(pull)[itex]\equiv[/itex]uB


$$\int f_{pull} \cdot dl = (uB) \frac{y}{cosθ}sinθ= vBhy$$



Problem: The vector f(pull) should be pointing outward (opposite the direction of wire pulling). so then shouldn't there be a negative sign somewhere?

--------------------


PART II


I decided to try and derive it my own way and i ran into a problem somewhere but i can't seem to spot where it is.


I said that, there is a vertical work component and a horizontal work component.

vertical work component

(From the initial pull)

$$W_y= \int (q\vec{v} \times \vec{B}) \cdot dy = (qvB)y= qvBy$$


horizontal work component

$$W_x= \int (q\vec{u} \times \vec{B}) \cdot dx = quBx =quBytanθ$$


vectorial sum

(yes i know work is a scalar quantity. but there is a work in x direction and work in the y direction so i thought i'd try this approach)

$$W= \sqrt{(qvBy)^2+(quBytanθ)2}= qBy\sqrt{v^2+u^2tan^2θ}$$

but since utanθ=v

$$W=qBy\sqrt{2v^2}=\sqrt{2}qvBy$$

i'm off by a factor of [itex]\sqrt{2}[/itex]


Could someone please help me find the mistake in doing it this way?


help is much appreciated. ty all!
 
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  • #2
Notice that on the left hand side is ##u\tan(\theta)## and on the right hand side is ##v##. So it must be that ##u\tan(\theta)=v##. Look at figure 7.11 to see why this might be
 
  • #3
Matterwave said:
Notice that on the left hand side is ##u\tan(\theta)## and on the right hand side is ##v##. So it must be that ##u\tan(\theta)=v##. Look at figure 7.11 to see why this might be


yeah i actually caught that right after i posted it. I'm actually now stuck with a different set of questions.

but thanks!
 

1. What is electrodynamics?

Electrodynamics is a branch of physics that studies the interaction between electric and magnetic fields. It describes how these fields affect charged particles and how they generate electromagnetic waves.

2. Who is Lorentz and what is his contribution to electrodynamics?

Hendrik Lorentz was a Dutch physicist who made significant contributions to the development of electrodynamics. He formulated the Lorentz force law, which describes the forces acting on a charged particle in an electric and magnetic field. He also proposed the Lorentz transformation, which forms the basis of Einstein's theory of special relativity.

3. Who is Faraday and what is his contribution to electrodynamics?

Michael Faraday was an English scientist who made groundbreaking discoveries in the field of electrodynamics. He discovered electromagnetic induction, which explains how a changing magnetic field can induce an electric current. He also proposed the concept of an electromagnetic field, which is essential to understanding the behavior of electric and magnetic fields.

4. What is the importance of electrodynamics?

Electrodynamics plays a crucial role in many modern technologies, such as electricity generation, communication systems, and medical imaging. It also helps us understand the fundamental laws of nature and has led to significant advancements in our understanding of the universe.

5. How is electrodynamics related to quantum mechanics?

Quantum electrodynamics is a field that combines quantum mechanics and electrodynamics to describe the behavior of particles at the atomic and subatomic level. It has been incredibly successful in predicting and explaining the behavior of particles and is essential in understanding many phenomena, including atomic and molecular structures, chemical bonding, and particle interactions.

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