Center of mass translation

[DandelionTheory]

(Given)

if the:

Center of gravity C is in the center of current I1

Blue X represents the direction of current I1, which is into the page

Red box represents an iron core

Green arrows represent magnetic fields due to I1 & I2 respectively 

Black circle next to I2 represents a wire loop with center axis perpendicular to current I1

Black circle next to I1 represents a cross section of wire in which I1 passes through the XY plane, the current loop I1 is not represented intentionally to ask this specific question.

 

B1 designates the magnetic field due to I1

 

B2 designates the magnetic field within the iron core due to I2

 

Assuming the force on I1 is a Lorentz force calculation with a small air gap between I1 and B2,

 

(Question)

how would one calculate the force and translation experienced by B2&I2, and is that force translated to net motion perpendicular to C(on the xy plane)or torque about the center of gravity?

"Debate the topic, not the language" -SomeoneSmarterThanMe

 

Edited March 23, 2020 by DandelionTheory

[Ghideon]

5 hours ago, DandelionTheory said:

(Question)

how would one calculate the force and translation experienced by B2&I2, and is that force translated to net motion perpendicular to C(on the xy plane)or torque about the center of gravity?

Hello! I find it tricky to analyse your question when only part of the setup is displayed. Is for instance the current I1 part of a current loop? Or is I1 some short-lived discharge? When calculating a "net effect" on some isolated system one need to know where the system boundaries are. 

Edited March 23, 2020 by Ghideon
clarification

[swansont]

The force on a current is IL x B where B is measured at the place where the current is. (often it's given as the force per unit length, so you can model an infinite wire -  F/L = I x B)

The right-hand rule gives you the direction

 

[DandelionTheory]

15 hours ago, swansont said:

The force on a current is IL x B where B is measured at the place where the current is. (often it's given as the force per unit length, so you can model an infinite wire -  F/L = I x B)

The right-hand rule gives you the direction

 

Thank you.

Just to confirm, 

The force on I1 is F=qE+I1xB2sin theta, where B2 is measured at I1

The force on I2 is F=I1LxBsin theta, where B1 is measured at I2 and theta is the angle between the current and interacting magnetic field.

Is my understanding correct?

I've seen videos where torque was described as rF=Mar, but you described it as F/r, I am confused. Please set me straight.

 

Edited March 24, 2020 by DandelionTheory

[DandelionTheory]

 

https://www.school-for-champions.com/science/force_torque.htm#.XnmML5BlA0N

[Ghideon]

4 hours ago, DandelionTheory said:

I've seen videos where torque was described as rF=Mar, but you described it as F/r, I am confused. Please set me straight.

Swansont is describing the force, not the torque. Force on an infinite wire as given by force per unit length:

19 hours ago, swansont said:

it's given as the force per unit length

Torque is "Force times the length of the lever arm. Or "Force times moment arm" as in your picture above. 

 

Edited March 24, 2020 by Ghideon

[DandelionTheory]

29 minutes ago, Ghideon said:

Swansont is describing the force, not the torque. Force on an infinite wire as given by force per unit length:

Torque is "Force times the length of the lever arm. Or "Force times moment arm" as in your picture above. 

 

Right, he answered part of it. I asked about a specific part to which no variables were stated in the answer. Unit length of what? How does it work into my problem? 

I'm not going to applause an answer if its incomplete.

[Ghideon]

23 minutes ago, DandelionTheory said:

I'm not going to applause an answer if its incomplete.

I tried to analyse your initial question, see my request for a clarification of the setup above. It is not clear which parts that are allowed to move relative to one another.

 

Edited March 24, 2020 by Ghideon
movement question added

[swansont]

2 hours ago, DandelionTheory said:

Right, he answered part of it. I asked about a specific part to which no variables were stated in the answer. Unit length of what?

Of whatever is carrying the current. The force on I1 will depend on the length of the wire and the magnetic field. The force on I2 will depend on the length of the wire and the magnetic field.

 

2 hours ago, DandelionTheory said:

How does it work into my problem? 

You have current-carrying wires, and you asked how to find the force

 

[DandelionTheory]

On 3/23/2020 at 11:48 PM, Ghideon said:

It is not clear which parts that are allowed to move relative to one another.

Pardon, I assumed stating the center of gravity was enough.

I assume force applied 90° from center of mass is transformed to torque through the center into the page. I needed clarification as to when torque was an applicable calculation.

On 3/24/2020 at 2:41 AM, swansont said:

Of whatever is carrying the current. The force on I1 will depend on the length of the wire and the magnetic field. The force on I2 will depend on the length of the wire and the magnetic field

Do I substitute L with 2πr^2 for each loop?

On 3/24/2020 at 2:41 AM, swansont said:

You have current-carrying wires, and you asked how to find the force

Thank you.

Is there torque about C due to the force on I2?

[swansont]

10 hours ago, DandelionTheory said:

Do I substitute L with 2πr^2 for each loop??

No, you can’t do that, because the cross product varies as you go around the loop, and the length would not depend on r^2. You have to integrate.