Understanding Linear Motors: Right Hand Rule & Current Flow

[TheWonderer1]

Hi there,

I attached an image of a basic linear motor. I'm a little confused if I use the right hand rule or left hand rule. I did it both ways and I think the left hand rule is the only rule that allows for a force being applied to the right. I assume the current is going down rather than upward like what it says in the left corner since the current moves clockwise.

Let me know if I'm correct on the rule and direction of the current. I'm assuming it moves through the coil in the middle.

 

[NFuller]

I attached an image of a basic linear motor. I'm a little confused if I use the right hand rule or left hand rule. I did it both ways and I think the left hand rule is the only rule that allows for a force being applied to the right. I assume the current is going down rather than upward like what it says in the left corner since the current moves clockwise.

I am not aware of any "left hand rule" only the right hand rule for determining the direction of the cross product of two vectors. In this scenario, you should apply the Lorentz force law to the charges traveling through the movable wire.

 

[TheWonderer1]

So when is the left hand rule usable? I've seen that it's for motor vs. right hand for generators. How do I apply the law with a magnetic field into the page and the current going up? It's just an example that I haven't seen.

 

[NFuller]

So when is the left hand rule usable? I've seen that it's for motor vs. right hand for generators.

I never use it. There may be some instances were it works for a specific problem, but the strict application of the right hand rule for cross products always works.

How do I apply the law with a magnetic field into the page and the current going up?

The Lorentz force law states
$$\mathbf{F}=q(\mathbf{E}+\mathbf{v\times B})$$
There is no electric field shown outside the wire so $\mathbf{E}$ is zero. The charges move in the direction of $\mathbf{I}$ and you know the direction of $\mathbf{B}$, so what is the direction of $\mathbf{F}$?

 

[TheWonderer1]

Is the current flowing upward? The magnet field is going into the page. I do the right hand rule and I find my palm facing away from me. My pointer finger is pointing down and my middle finger is away from me. The force is to the right.

However, do you use the thumb is the current direction, field are your fingers and your palm faces the force direction? It's all confusing because there are several ways to do it.

 

[NFuller]

Is the current flowing upward?

It appears that it is flowing downward through the movable rail. To use the right hand rule, extend your fingers on your right hand in the direction of the first vector $\mathbf{v}$, now adjust your hand such that you can curl your finders in the direction of the second vector $\mathbf{B}$. Your thumb should now point in the direction of the cross product $\mathbf{F}$.