# Magnetic force and torque

#### kidia

I have a question here

A rectangular plane loop with dimensions 250 mm by 180 mm is pivoted to rotate about the z axis. The long side of the loop is along the y-axis and the plane of the loop makes an angle of 45 degrees with the y-axis. If a uniform magnetic field of magnitude 300 mT is in the y direction: (a) Determine the magnitude and direction of the force of each side of the loop. (b) Determine the torque about the z axis.

I know that F=BILsin theta and Torque=BAIsin theta my problem here is how to get the current I

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#### rtharbaugh1

Probably no one here will give you the answer because this sounds like a homework problem and you should not expect others to do your homework for you.

R

#### kidia

Please Rtharbaugh1 if this problem is challenging to you,leave others to work on it.

#### Hootenanny

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Think about using simultaneous equations Write down what you know and what you want to know.

#### nrqed

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kidia said:
I have a question here

A rectangular plane loop with dimensions 250 mm by 180 mm is pivoted to rotate about the z axis. The long side of the loop is along the y-axis and the plane of the loop makes an angle of 45 degrees with the y-axis. If a uniform magnetic field of magnitude 300 mT is in the y direction: (a) Determine the magnitude and direction of the force of each side of the loop. (b) Determine the torque about the z axis.

I know that F=BILsin theta and Torque=BAIsin theta my problem here is how to get the current I
As far as I can tell, there is no way to answer without additional input. You are right, we need to be able to find the current and we can't with only this. Are you sure you copied the entire problem???

#### Hootenanny

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nrqed said:
As far as I can tell, there is no way to answer without additional input. You are right, we need to be able to find the current and we can't with only this. Are you sure you copied the entire problem???
I disagree, you have the flux density, the length of the conductor, the angle, the area of the conductor, you can also calculate the distance from the pivot to the applied force, thus you can equate the two formulas stated.

That's how I see it, if I'm missing something (likely) please let me know.

#### nrqed

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Hootenanny said:
I disagree, you have the flux density, the length of the conductor, the angle, the area of the conductor, you can also calculate the distance from the pivot to the applied force, thus you can equate the two formulas stated.

That's how I see it, if I'm missing something (likely) please let me know.
I am not sure what you mean by flux density. I did not notice any information about magnetic flux or flux density...

Regards

Pat

#### Hootenanny

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kidia said:
If a uniform magnetic field of magnitude 300 mT is in the y direction:
Flux density is measure in Tesla's (T), therefore the magnetic flux density is 300 mT. The two unknows in the equations Kidia posted are Force and Current. You can eliminate force and thus calculate the current.

#### nrqed

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Hootenanny said:
Flux density is measure in Tesla's (T), therefore the magnetic flux density is 300 mT. The two unknows in the equations Kidia posted are Force and Current. You can eliminate force and thus calculate the current.

Ok...Thanks. It's the first time that I see the magnetic field called this way

But he still cannot solve without more input. There are *3* unknowns in his two equations: I, F and the torque. he is asked to find the force and the torque so I assume that the current must be provided in the question. without that, there is no way to calculate the force and teh torque.

Patrick

#### Hootenanny

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nrqed said:
Ok...Thanks. It's the first time that I see the magnetic field called this way

But he still cannot solve without more input. There are *3* unknowns in his two equations: I, F and the torque. he is asked to find the force and the torque so I assume that the current must be provided in the question. without that, there is no way to calculate the force and teh torque.

Patrick
Toreque can be expressed as force time distance from the pivot ($\tau = Fd$). If we assume that the coil is pivoted in the middle of the short side, we can say that d = 90mm. Thus, this leaves the unkowns as I and F. I know you have to make an assumption, but I think it is a valid one.

#### nrqed

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Hootenanny said:
Toreque can be expressed as force time distance from the pivot ($\tau = Fd$). If we assume that the coil is pivoted in the middle of the short side, we can say that d = 90mm. Thus, this leaves the unkowns as I and F. I know you have to make an assumption, but I think it is a valid one.
I know, but this equation is not linearly independent of the two already given! (use this with the equation for the force and you will end up with the equation for torque already given!). So no new information there.

I challenge you (in a friendly way) to find numerical values for F and $\tau$ with no value of the current provided :shy:

#### Hootenanny

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I (friendly) accept your challange sir

#### Hootenanny

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Nrqed, I conceed. You are quite right, the current is required.

#### nrqed

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Hootenanny said:
Nrqed, I conceed. You are quite right, the current is required.
:shy: Thanks for being fair play!

"Magnetic force and torque"

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