Imaginary value for magnetic field?

[Hawksteinman]

[Mod Note: Thread moved from Classical Physics, hence no formatting template]

So today we performed an experiment to measure the Earth's magnetic field in three dimensions. For one of the dimensions we got 6.6x10^-5 i

We were wondering if an imaginary magnetic field was possible and what it would mean. The resultant magnetic field was a real field.

We did sqrt (Ux - Uy + Uz) / 2a but Uy was larger than Ux + Uz. Is this a mistake in the measurement or is Earth's magnetic field imaginary in some places?

(Can't format equations on my phone)

 

[BvU]

My guess is that $\hat\imath$ is a unit vector in one of the three directions (the others then would be $\ \hat\jmath$ and $\hat k\$), not the imaginary number $i$.

( another possible explanation is that the display wanted to show a capital $T$ but a few segments were broken ...)

You did

sqrt (Ux - Uy + Uz) / 2a

for some reason (other than that it was in the instructions) ?

 

[Hawksteinman]

My guess is that $\hat\imath$ is a unit vector in one of the three directions (the others then would be $\ \hat\jmath$ and $\hat k\$), not the imaginary number $i$.

( another possible explanation is that the display wanted to show a capital $T$ but a few segments were broken ...)

You did
for some reason (other than that it was in the instructions) ?

Those 3 U's were squared I think, actually

And yeah it was in the instructions. I did it step by step and before I square rooted I got a negative number so I knew it was imaginary.

 

[Hawksteinman]

Those 3 U's were squared I think, actually

And yeah it was in the instructions. I did it step by step and before I square rooted I got a negative number so I knew it was imaginary.

Also the a was squared as well

 

[BvU]

And yeah it was in the instructions

Any idea why it was in the instructions ? Typo ?
(Good thing it didn't say 'jump in the lake' ! )

Let's move this to homework and use the template. You can explain what U_x, U_y, U_z, $\$ a $\$ are and what your results for each of them were.
Oh, and where the .66 Gauss popped up, too...

Homework Statement

Homework Equations

The Attempt at a Solution

[/B]

 

[Hawksteinman]

Any idea why it was in the instructions ? Typo ?

(Good thing it didn't say 'jump in the lake' ! )Let's move this to homework and use the template. You can explain what U_x, U_y, U_z, $\$ a $\$ are and what your results for each of them were.

Homework Statement

Homework Equations

The Attempt at a Solution

[/B]

Ok well I don't have the work with me because we had to hand it in but I'll try from memory :)We had a rotating solenoid with 320 coils and we measured the time period of the oscillation and the amplitude of the voltage sine wave. U_x was the amplitude when the coil was rotating along the x dimension.We then used Pythagoras in 3 dimensions.B_y = sqrt((U_x² - U_y² + U_z²)/2a²)Where a = (2pi²NR²)/TThe thing is our value for B_y was imaginary :/

 

[Charles Link]

They would do well to show you what they are doing with the measurement, instead of simply plugging in some numbers into a formula whose origin they don't explain to you. If you have a magnetic field whose strength (and direction) is known, you can cause a magnetic moment such as a compass needle to line up with that magnetic field. If the compass needle shows any deviations from being aligned with the applied magnetic field, the deviation/deflection would be caused the Earth's magnetic field. I believe the experiment that you did was something that of this nature, but they need to show you more detail.

 

[Hawksteinman]

They would do well to show you what they are doing with the measurement, instead of simply plugging in some numbers into a formula whose origin they don't explain to you. If you have a magnetic field whose strength is known, you can cause a magnetic moment such as a compass needle to line up with that magnetic field. If it shows any deviations from being aligned, the deviation could be attributed to the Earth's magnetic field. I believe the experiment that you did was something that of this nature, but they need to show you more detail.

We had to figure it out for ourselves and we were being marked on whether we could do it or not. I understand what happened but I'm concerned about the imaginary value :/

The lecturer said not to worry about it because imaginary numbers are used in physics all the time but I'm wondering about what it means physically :/

 

[Charles Link]

We had to figure it out for ourselves and we were being marked on whether we could do it or not. I understand what happened but I'm concerned about the imaginary value :/

The lecturer said not to worry about it because imaginary numbers are used in physics all the time but I'm wondering about what it means physically :/

In this case it seems like an incorrect formula and/or experimental error. The information you have supplied is insufficient to do much more with it.

 

[Hawksteinman]

In this case it seems like an incorrect formula and/or experimental error. The information you have supplied is insufficient to do much more with it.

The graph was plotted by a computer every millisecond and the slightest disturbance could affect its measurement (it was measuring to the nearest 0.001 milliVolts) so it could be a disturbance I guess :/

 

[BvU]

when the coil was rotating along the x dimension

I suppose you think that we know what your x-axis is, but here my teplepathic capabilities fail me. Is it east-west and do you mean that the axis of the coil with 320 turns is in the vertical north-south plane ?

We had to figure it out for ourselves and we were being marked on whether we could do it or not

so, contrary to post #3,

sqrt (Ux - Uy + Uz) / 2a

was not in the instructions, but you derived it somehow. How ?

 

[Hawksteinman]

I suppose you think that we know what your x-axis is, but here my teplepathic capabilities fail me. Is it east-west and do you mean that the axis of the coil with 320 turns is in the vertical north-south plane ?
so, contrary to post #3,
was not in the instructions, but you derived it somehow. How ?

Well we were told to use this machine and these equations, basic instructions on how to use it, and no help was allowed once we started so we ended up spending 30 minutes figuring it out :/

And we don't know what the x-axis was it was perpendicular to the table we were using, and that's all :/

 

[Hawksteinman]

Well we were told to use this machine and these equations, basic instructions on how to use it, and no help was allowed once we started so we ended up spending 30 minutes figuring it out :/

And we don't know what the x-axis was it was perpendicular to the table we were using, and that's all :/

The x-axis would be the axis along which the coil is rotating

 

[Charles Link]

You might find it of interest that using a simple boy scout compass,and using the known value of the Earth's magnetic field, you can get an approximate measurement of the magnetic field strength of a simple bar magnet (at a given distance). Likewise, if you know the magnetic field strength of a given magnet, you could compute the strength of the Earth's magnetic field (the horizontal component) from observing the direction of the compass needle and its deviation from north as the magnetic field from the magnet is applied. See post 21 of the following "link": https://www.physicsforums.com/threa...re-relationship-in-ferromagnets.923380/page-2

 

[BvU]

Ok well I don't have the work with me because we had to hand it in but I'll try from memory :)We had a rotating solenoid with 320 coils and we measured the time period of the oscillation and the amplitude of the voltage sine wave. U_x was the amplitude when the coil was rotating along the x dimension.We then used Pythagoras in 3 dimensions.B_y = sqrt((U_x² - U_y² + U_z²)/2a²)Where a = (2pi²NR²)/TThe thing is our value for B_y was imaginary :/

Homework Statement

Good. I can guess what R is, and T. You might explain the 'Pythagoras in 3D' to us. I find it hard to understand where the asymmetry comes from, but who knows.

Perhaps a few sketches of the setup would help too.
And the measured values ? 0.001 mV brings you well into the realm of noise from other sources if unfortunate wiring works like an antenna.Furthermore, is B_y meant to be the vertical component ? ( If there is only a vertical component, I can understand U_x=U_y and U_z=0 )

How was the coil rotated ?

 

[BvU]

The x-axis would be the axis along which the coil is rotating

That does not help. Draw a picture. A coil rotates around an axis, not along an axis. And is x east in your experiment, or is it north ?

 

[Hawksteinman]

Homework Statement

Good. I can guess what R is, and T. You might explain the 'Pythagoras in 3D' to us. I find it hard to understand where the asymmetry comes from, but who knows.

Perhaps a few sketches of the setup would help too.
And the measured values ? 0.001 mV brings you well into the realm of noise from other sources if unfortunate wiring works like an antenna.Furthermore, is B_y meant to be the vertical component ? ( If there is only a vertical component, I can understand U_x=U_y and U_z=0 )

How was the coil rotated ?

The above equation was pointed out by one of the other students to be basically Pythagoras in 3 dimensions :/

The coil was rotated by a motor and had to be rotated backwards after each measurement due to the wires wrapping around it :/

We actually used B_z as the vertical component :/

 

[Hawksteinman]

Maybe we were supposed to use B_y as the vertical but we used B_z instead :(

 

[Hawksteinman]

Maybe we were supposed to use B_y as the vertical but we used B_z instead :(

So our values for B_y and B_z where the wrong way round :(

So when we used the equation we got the wrong result and ended up with an imaginary number

 

[Hawksteinman]

That does not help. Draw a picture. A coil rotates around an axis, not along an axis. And is x east in your experiment, or is it north ?

We didn't check which was North or East :(

 

[Delta2]

Well I am not sure I understand the whole method (coil rotating around some axis to measure the B-Field using the induction effect I guess), why in the Pythagoras 3D you use $...-{U_y}^2...$ and not $+{U_y}^2$, but what I got to say is that the value of magnetic field B or any of its components Bx,By,Bz cannot be imaginary. Imaginary numbers quite often have physical meaning in physics (like for example when we use an imaginary number for the impedance of a coil or a capacitor in AC current/voltage calculations) but not in this case.

Because I see you got a very small number of the order of 10^-5 (squared is of the order 10^-10 quite small) maybe it was meant to be zero and noise in the measurements made it slightly negative and hence the square root , slightly imaginary. In what units of magnetic field is the measurement result made?

 

[Hawksteinman]

Well I am not sure I understand the whole method (coil rotating around some axis to measure the B-Field using the induction effect I guess), why in the Pythagoras 3D you use $...-{U_y}^2...$ and not $+{U_y}^2$, but what I got to say is that the value of magnetic field B or any of its components Bx,By,Bz cannot be imaginary. Imaginary numbers quite often have physical meaning in physics (like for example when we use an imaginary number for the impedance of a coil or a capacitor in AC current/voltage calculations) but not in this case.

Because I see you got a very small number of the order of 10^-5 (squared is of the order 10^-10 quite small) maybe it was meant to be zero and noise in the measurements made it slightly negative and hence the square root , slightly imaginary. In what units of magnetic field is the measurement result made?

Micro Teslas

 

[Delta2]

Micro Teslas

Well that's pretty small units but still By could be zero or very close to zero, if y is the direction perpendicular to Earth's surface ( the radial direction). The magnetic field of Earth is almost tangential to Earth's surface (viewing Earth surface's as a perfect sphere).

 

[Hawksteinman]

Well that's pretty small units but still By could be zero or very close to zero, if y is the direction perpendicular to Earth's surface ( the radial direction). The magnetic field of Earth is almost tangential to Earth's surface (viewing Earth surface's as a perfect sphere).

Our By was parallel to Earth, value of about 0.066 milli Tesla while Bx (parallel) was 0.74 milli Tesla and Bz (perpendicular) was 0.82 milli Tesla (approximately) :/

 

[Hawksteinman]

Our By was parallel to Earth, value of about 0.066 milli Tesla while Bx (parallel) was 0.74 milli Tesla and Bz (perpendicular) was 0.82 milli Tesla (approximately) :/

So it was 66 micro Teslas

 

[Charles Link]

To calculate the correct answer, try this: https://www.ngdc.noaa.gov/geomag-web/#igrfwmm You need to click on the 3rd tab near the top="Magnetic Field". I was surprised to find about 50 micro Tesla is a vertical component pointing downward at my geographic location (Chicago), and only about 20 micro Tesla points northward in the horizontal plane.$\\$ You might want to check your decimal place also=.82 milli Tesla is 820 micro Tesla and that is too large.

 

[Hawksteinman]

These are the equations we used

 

[Delta2]

In my opinion $B_z$ contains big error in measurements , it just can't be that large (unless you did measurements above a room with electric generators)

$B_y$ also has some small error in measurement, should ve been small positive but it ended up small negative.

Don't know about $B_x$.