How does this make any sense to anyone? I'm trying to find

[math]\vec{F} = q\vec{E} + q\vec{v} \times \vec{B}[/math]

is the law for a single point particle with charge q. If the electric field is taken to be zero (E = 0) then it becomes

[math]\vec{F} = q\vec{v} \times \vec{B}[/math]

Now consider a small infinitesimal part of a wire with many electrons flowing through it with no external electric field. The new form of the law becomes

[math]d\vec{F} = Id\vec{l} \times \vec{B}[/math]

You can now integrate it to get

[math]\vec{F} = I\vec{l} \times \vec{B}[/math]

This lets you talk about wires instead of point particles.

You should be able to convince yourself that both ways of writing it are equivalent. The charge (in Coulombs) times velocity (in meters/second) is equal to the current (in Coulombs/second) times length (in meters).

>>8124736
>How does this make any sense to anyone?
It barely does. It is an attempt to simplify the complex relationship between moving charge (current), magnetic field and force. All three are vectors in 3D space with an orthogonal relationship. Hence the left-hand / right-hand motor /generator rules.
It's all about a magnet and conductor, move them and a current is produced, run a current thru the conductor and motion is produced.
then you get people like
>>8124866
who give near non-sense statements like
>a wire with many electrons flowing through it with no external electric field
A current with no accompanying electric field? I hate to break it to you but this rarely happens in the real world. Electric and magnetic fields are inseparable from current flow in the real world. These "special cases" are to simplify a very, very complex equation (maxwell's) into an engineering ready equation that can be used to approximate special real world conditions.
The real fun comes when you realize that a real world motor also acts as a generator, generating in the wrong direction and a real world generator also has motor action with the torque acting as drag along with the mechanical losses. The true engineering is in reducing these factors.

It also gets interesting when you realize that magnetic forces have complex force vectors that have torque component (cw / ccw and magnitude) as well as the ordinary linear component of direction and magnitude.
This results in magnetic fields only being able to transfer physical force along two of the three axis.

>>8124736
> How does this make any sense
What is "this"?

The equation for (the magnetic component of) the Lorentz force (F=q(B×v)=B×I), or the mnemonic using fingers?

The Lorentz force doesn't "make sense". It's just how the universe happens to be. Physics isn't math; you can't derive it from first principles, you just have to make empirical observations and describe the results.

One of those results is that the force on a charged particle moving in a magnetic field is equal to the charge (a scalar) multiplied by the cross product (a vector) of the magnetic field and the velocity.

>>8124736
your index fingers and how they naturally curl are the magnetic field lines. Your thumb is the direction of force experienced by the conductor, and the direction your palm (perpendicularly out of your palm) is facing is the flow of current.

what is confuse about this?

Experiment, make observations, make definitions.

We can use our hands to remember how a charged particle reacts to magnetic fields.

What exactly is it that you don't get?

>>8125944
that it's bullshit psuedopscience, that's what.

>>8127353
undergrad who failed physics 2 detected

Are there any four-dimensional variants of this in physics?

>>8127577
I don't think so, there is no cross product in four dimensions.
Or what do you mean exactly?

>>8127524
You're gonna fucking tell me that this isn't just an extreme simplification of vectors, which does indeed border on being pseudoscience?

>>8128109
a practical visual-aid to the legitimate right-handed cross product that produces the correct physical (or if you like, empirical) results is not the same as selling homeopathic 'healing' supplements or claiming some ridiculous quantum consciousness nonsense, my friend.

Visual guides are quite useful, especially a nice 3D model so 'handy' as this one, when you're wondering about vector operations and their physical effects. No need to be upset.

>>8125635
>you can't derive physics from first principles

are you dumb. Thats literally the point of any high level mathematical physics right now. The Hierarchy problem is literally this.

>>8128109
Man that's just the way the universe works.

We define clockwise and counter clockwise rotation around a vector (quaternion-like).

either we can introduce the 6th graders to quaternions or we can say, just use your fingers and hand as a guide.

Besides being able to model complex ideas as simple ideas is what got us to the point we're at.

Even the idea of quaternion rotation being represented as it is, is itself a useful model.

Just like OP and his hand gesture-force direction method

>>8128175
You know what? You're right.

>>8128160
you are literally retarded