# Help with magnetic field forces in a motor

• Engineering
Hi all,

Not a question about completing homework here, but I'm a teacher looking to create a realistic engineering question for an assignment.

I have an engineering scenario I've set for the assignment which is a junior engineer working for a marine engineering company so all of the questions on my assignment are relating to the development of a prototype marine research vessel.

I'm a bit stumped on the section for vectors. I will have the standard ship going one way, current going another... BUT...

I also want to cover cross product and dot product.

For cross product, I'd like to ask a question relating to the ship's diesel-electric propellers. In particular, I'd like to ask a question about the force exerted to rotate the prop shaft on an azimuth pod supplied with 6.6kV of AC power.

I believe the equation I want to use is this one:
$\overrightarrow{F}=q\overrightarrow{v}\times \overrightarrow{B}$

Now, my problem is, I don't know much about motors in a real-world context so I'm not sure what vector values to use for this question to make it realistic. Does anyone have any suggestions? I can't seem to find any useful information about how strong the magnets in the motor would be or what velocity to expect the current to move through the coils. I know I don't have details about the wire gauges involved but a ballpark figure would be sufficient.

Any suggestions for dot product questions would also be great!

Also, it's 2:30 in the morning so I could be way off base with this all together :)

Any suggestions would be greatly helpful!

Many thanks!
Chris

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Delta2
Homework Helper
Gold Member
The equation you mention tell us what happens in the individual charge carriers (the moving electrons inside the current carrying coils of the electric motor).

It will be better to use the macroscopic version of the equation which is $\vec{F}=I\vec{l}\times \vec{B}$ (1) where $I$ is the current in the rotating coils (rotor) of the motor and $\vec{l}$ is a vector that you can take it to be the axis of the motor, and F is the force in one turn of a coil. This doesn't mean that the force from the magnetic field is applied to the axis of the motor, it is applied to each turn of the rotating coil. Also as the coil rotates the force varies and also the torque of the force varies from 0 to a maximum value.

However an electric motor can have multiple coils and each coil with multiple turns, so that Force from eq. (1) is actually multiplied by the number of coils and by the number of turns of each coil.

And have in mind what I just said is just an approximation, in order to accurately calculate F we need to know the shape and size of the coils and how each coil is positioned relative to each other.

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The equation you mention tell us what happens in the individual charge carriers (the moving electrons inside the current carrying coils of the electric motor).

It will be better to use the macroscopic version of the equation which is $\vec{F}=I\vec{l}\times \vec{B}$ (1) where $I$ is the current in the rotating coils (rotor) of the motor and $\vec{l}$ is a vector that you can take it to be the axis of the motor, and F is the force in one turn of a coil. This doesn't mean that the force from the magnetic field is applied to the axis of the motor, it is applied to each turn of the rotating coil. Also as the coil rotates the force varies and also the torque of the force varies from 0 to a maximum value.

However an electric motor can have multiple coils and each coil with multiple turns, so that Force from eq. (1) is actually multiplied by the number of coils and by the number of turns of each coil.

And have in mind what I just said is just an approximation, in order to accurately calculate F we need to know the shape and size of the coils and how each coil is positioned relative to each other.

Ah yes, that makes more sense, now that I've slept!

If you have a way of setting up a problem like this, I'd certainly love to see it. My skills are in the computation, my lack of knowledge of the inner workings of a motor are my weakness, but I'm required to put these things in real-world settings which isn't always easy for me since I have no experience working with vector forces in my former professional life. I was just an electronics technician who changed components and did soldering to repair things.

Would it be best to just use a torque formula?

Delta2
Homework Helper
Gold Member
Well to tell you the truth, I haven't deal myself a lot with the inner workings of a motor neither with a lot motor problems , I just know some basic fundamental theory. I doubt i can setup a satisfying problem where i ll give some data and ask to calculate maximum/average force or maximum/average torque.

Maybe it would be nice for you to read the Wikipedia article on electric motors https://en.wikipedia.org/wiki/Electric_motor

The image at the top right of the articles says a lot, you can see the two permanent magnets marked as N and S that create the permanent magnetic field (the $\vec{B}$ in equation 1.) Also you can see the two rotating coils in the rotor, the blue and the red coil in the rotating part. Unfortunately it doesn't show in the animation the vectors of the Forces on the coils and of the Torques of these forces.

I think the most important part of the article is here https://en.wikipedia.org/wiki/Electric_motor#Components where it describes the basic components of any electric motor.

I ll just mention @rude man and @berkeman here that have a master in electric engineering and probably know a lot more about motors, I am just a mathematician after all. Maybe also @jim hardy can be of assistance.

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Thanks!

I think I'm gonna go with a more accessible problem for me. Just going to deal with a torque force on the ship's pivot point when the rudder is applied in a certain angle, will fit with the scenario and be easier to create a problem for it :)