In summary, electric generators work by applying the Lorentz force on a conductor moving at a velocity v in the presence of a magnetic field B. The emf is equal to -Blv. This voltage is intended to move current in the conductor to produce an induced magnetic field so that it opposes the change in the magnetic field through the conductor.
I'm trying to understand how electric generators work on a very basic level. I understand the heart of this is the application of the Lorentz force on a conductor moving at a velocity ##v## in the presence of a magnetic field ##B##. I also understand how it can be shown that the emf is equal to ##-Blv## where ##l## is the length of the conductor.

Now, this emf corresponds to the separation of charges (positive charges pile up at the top and negative charges pile up at the bottom) due to the Lorentz force, which is then balanced by the Coulombic attraction between the positive and negative charges. I also understand that the negative sign comes from Lenz's law, which says that this voltage that is developed is intended to move current in the conductor to produce an induced magnetic field so that it opposes the change in the magnetic field through the conductor.

I would expect the top of the conductor to be more positive relative to the bottom. But if ##V = -Blv##, then the voltage at the top is more negative relative to the bottom? That part confuses me. What confuses me further is that this negative sign is commonly discarded. Consider for example, this at 7 minutes.

Why is this allowed? Isn't the negative sign crucial to labeling how charges move through the conductor and ultimately through a generator? I know that a generator involves multiple linked segments of conductors that push the charges around a loop with two sides being responsible for the total voltage being developed at the terminals of the generator. So, I would think preserving the minus sign in calculating the total voltage generated at the terminals of a generator would be important.

Thanks in advance for the help.

I want to show a diagram of my own that really illustrates the heart of what I'm confused about.

Basically, the Lorentz force should make positive charges go up top, but ##V_{\ell} = -Bv\ell## implies that the top is more negative than the bottom. How is this possible? Where does the contradiction come from?

Basically, the Lorentz force should make positive charges go up top, but Vℓ=−BvℓV_{\ell} = -Bv\ell implies that the top is more negative than the bottom. How is this possible? Where does the contradiction come from?
No , it doesn't . When you move along the direction of electric field , does potential drop increase or decrease ?
Hint : - ∫ E.dl = ΔV . Check your integration in your second post .

As you move along the direction of the electric field, the potential drops because the field is doing work on you. I am not sure what is wrong with the integration.

Last step , left hand side - to first on the right - it would be V0 - Vl .

Hope this helps .

Why is it ##V_0 - V_l## and not ##V_i - V_0##? I thought the definition of voltage was
$$V_{\text{final}} - V_{\text{initial}} = -\int_{\text{initial}}^{\text{final}} E \cdot dl$$

Yes , but in this case , you are moving in a direction opposite to electric field .

That makes perfect sense. That is where the extra negative sign comes from. So, that means ##V_{\ell} = B\ell v## in the end. I wonder if those teachers / professors in those YouTube videos / lectures were all assuming something about the B field and just forgetting to include it? It feels like misinformation to say ##V_{\ell} = -B\ell v## then.

Qwertywerty

## 1. What is motional EMF?

Motional EMF, or electromotive force, is the voltage generated in a conductor when it moves through a magnetic field.

## 2. How is motional EMF calculated?

Motional EMF is calculated using the equation E = -vBℓ, where E is the EMF, v is the velocity of the conductor, B is the magnetic field strength, and ℓ is the length of the conductor.

## 3. Why is the minus sign in the equation for motional EMF?

The minus sign in the equation for motional EMF indicates that the induced current flows in a direction that opposes the motion of the conductor. This is known as Lenz's Law.

## 4. What are some real-world applications of motional EMF?

Motional EMF is used in devices such as generators, motors, and microphones. It is also a key concept in understanding electromagnetic induction, which is used in power generation and transformers.

## 5. How does motional EMF relate to Faraday's Law?

Motional EMF is a result of Faraday's Law, which states that a changing magnetic field will induce an electric field. In the case of motional EMF, the changing magnetic field is caused by the motion of the conductor through the field.

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