EMF due to Lorentz electric and magnetic forces

[songoku]

Homework Statement

This is not homework.

I want to understand the difference between emf generated due to Lorentz electric and magnetic force.

Relevant Equations

F = E.q

F = Bqv sin θ

$E=-N \frac{d\phi}{dt}$

Φ = BA cos θ

Example of emf due to Lorentz magnetic force is motional emf. When rod PQ moves to the left, there will be downwards magnetic force acting on the positive charge in the rod PQ so point Q is at higher potential compared to point P so there will be potential difference (emf) between P and Q

The formula of Lorentz electric force is F = Eq. But I don't understand how this force can create emf. What is the example of emf generated due to Lorenzt electric force?

Thanks

 

[Steve4Physics]

The formula of Lorentz electric force is F = Eq. But I don't understand how this force can create emf. What is the example of emf generated due to Lorenzt electric force?

Hi @songoku.

We don’t usually think of an emf being produced by an electric force. It is more common to deal with the reverse situation - where an emf produces an electric force (e.g. a cell pushing electrons through a lamp).

However, one example is this:

A cell has an emf. In principle, inside the cell, we can think of internal electrons being pushed by the cell’s internal electric field (existing between atoms/ions). The electric force (F=qE) act on the electrons inside the cell. This force piles the electrons onto the cell’s negative terminal and pulls electrons from the cell’s positive terminal. That’s how the cell’s emf is created by the internal electric force.

Not a good example, because what happens inside a cell is much more complex. Maybe someone will have a better example.

Note:
An energy supply is needed to create an emf.
For the cell, the energy supply is in the chemicals.
For a ‘dynamo’, the energy supply is whatever is doing work, pushing the moving parts.

 

[Delta2]

Whether we have motional EMF or transformer EMF it is due to separation of charges in the two ends. The cause of this separation of charges is different in the two cases:

• In motional EMF the cause of separation of charges is the force $(v\times B)q$
• In transformer EMF the cause of separation of charges is the force $E_{NC}q$ where $E_{NC}$ the non conservative component of the electric field that is produced by the time varying magnetic field according to the Maxwell-Faraday equation :$$\nabla\times E_{NC}=-\frac{\partial B}{\partial t}$$

 

[songoku]

Hi @songoku.

We don’t usually think of an emf being produced by an electric force. It is more common to deal with the reverse situation - where an emf produces an electric force (e.g. a cell pushing electrons through a lamp).

However, one example is this:

A cell has an emf. In principle, inside the cell, we can think of internal electrons being pushed by the cell’s internal electric field (existing between atoms/ions). The electric force (F=qE) act on the electrons inside the cell. This force piles the electrons onto the cell’s negative terminal and pulls electrons from the cell’s positive terminal. That’s how the cell’s emf is created by the internal electric force.

Not a good example, because what happens inside a cell is much more complex. Maybe someone will have a better example.

Note:
An energy supply is needed to create an emf.
For the cell, the energy supply is in the chemicals.
For a ‘dynamo’, the energy supply is whatever is doing work, pushing the moving parts.

Hi Steve

I kinda get your example. Actually in my mind I have other question. I always relate emf produced to change in Φ (based on Faraday law) so it is hard for me to understand the relation of electric force and ΔΦ / Δt. Maybe my current knowledge is not enough to understand it in deeper level

Whether we have motional EMF or transformer EMF it is due to separation of charges in the two ends. The cause of this separation of charges is different in the two cases:

• In motional EMF the cause of separation of charges is the force $(v\times B)q$
• In transformer EMF the cause of separation of charges is the force $E_{NC}q$ where $E_{NC}$ the non conservative component of the electric field that is produced by the time varying magnetic field according to the Maxwell-Faraday equation :$$\nabla\times E_{NC}=-\frac{\partial B}{\partial t}$$

With this post, it is certain that my knowledge is not sufficient

What I know about transformer is only the emf produced in secondary coil is due to the secondary coil cuts the time varying magnetic field produced by primary coil because of time varying current flowing through it. I never even heard about non conservative component of electric field

Thank you very much for the help and explanation Steve4Physics and Delta2