## Circuit Lab B/C

Test your knowledge of various Science Olympiad events.
Crimesolver
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### Re: Circuit Lab B/C

Ohhh okay

How do you find the strength of an electromagnetic field?

What would be the strength of the magnetic field if the electromagnet was 200 cm, has 10 amps running through it, and has 400 coils?
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MattChina
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### Re: Circuit Lab B/C

Crimesolver wrote:Ohhh okay

How do you find the strength of an electromagnetic field?

What would be the strength of the magnetic field if the electromagnet was 200 cm, has 10 amps running through it, and has 400 coils?

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Crimesolver
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### Re: Circuit Lab B/C

MattChina wrote:
Crimesolver wrote:Ohhh okay

How do you find the strength of an electromagnetic field?

What would be the strength of the magnetic field if the electromagnet was 200 cm, has 10 amps running through it, and has 400 coils?

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UTF-8 U+6211 U+662F
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### Re: Circuit Lab B/C

Reviving... what does Coulomb's law state?

MattChina
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### Re: Circuit Lab B/C

UTF-8 U+6211 U+662F wrote:Reviving... what does Coulomb's law state?

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### Re: Circuit Lab B/C

MattChina wrote:
UTF-8 U+6211 U+662F wrote:Reviving... what does Coulomb's law state?

MattChina
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### Re: Circuit Lab B/C

Question
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### Re: Circuit Lab B/C

MattChina wrote:
Question

MattChina
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### Re: Circuit Lab B/C

UTF-8 U+6211 U+662F wrote:
MattChina wrote:
Question

No, there are some cases where they don't apply. With KVL, it doesn't apply with a varying magnetic field, and with KCL, it doesn't apply when the voltage source has a very high frequency. Anyways, your turn!
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### Re: Circuit Lab B/C

MattChina wrote:
UTF-8 U+6211 U+662F wrote:
MattChina wrote:
Question

No, there are some cases where they don't apply. With KVL, it doesn't apply with a varying magnetic field, and with KCL, it doesn't apply when the voltage source has a very high frequency. Anyways, your turn!

Whoops...

Calculate the electric field strength 1 micrometer from a proton (e=1.6e-19 C).

If a proton is moving east at 300 m/s and experiences an acceleration of 2.6e10 m/s^2 south, what is the strength and direction of the B-field (the mass of a proton is 1.67e-27 kg)?

mdv2o5
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### Re: Circuit Lab B/C

MattChina wrote:
UTF-8 U+6211 U+662F wrote:
MattChina wrote:
Question

No, there are some cases where they don't apply. With KVL, it doesn't apply with a varying magnetic field, and with KCL, it doesn't apply when the voltage source has a very high frequency. Anyways, your turn!

So this isn't relevant to the next question, but I think it's informative to clarify the statement about KVL not holding. The issue seems a bit more complicated than KVL being invalid in some cases. KVL ostensibly doesn't hold in the situations mentioned above because there are parasitic inductances that come into play that the normal lumped element model of resistors does not take into account. If the model is made more realistic by adding in these inductances and we are careful with how we define voltages and KVL, then indeed, KVL still holds within a varying magnetic field or with high frequency sources since it is dependent on a conservation of energy argument. It ultimately boils down to the model being insufficient to explain everything that is happening in the circuit rather than a problem with KVL.

This issue actually turned into quite a big discussion online which resulted in a very in-depth look at a series of definitions and experiments. A whole lot more can be found at the following places:
ElectroBOOM's Initial Assertion
Followup video
Relevant paper by MIT Professor John Belcher in response

In any case, sorry about the interruption to the question chain. Please carry on.

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### Re: Circuit Lab B/C

mdv2o5 wrote:
MattChina wrote:
UTF-8 U+6211 U+662F wrote:

No, there are some cases where they don't apply. With KVL, it doesn't apply with a varying magnetic field, and with KCL, it doesn't apply when the voltage source has a very high frequency. Anyways, your turn!

So this isn't relevant to the next question, but I think it's informative to clarify the statement about KVL not holding. The issue seems a bit more complicated than KVL being invalid in some cases. KVL ostensibly doesn't hold in the situations mentioned above because there are parasitic inductances that come into play that the normal lumped element model of resistors does not take into account. If the model is made more realistic by adding in these inductances and we are careful with how we define voltages and KVL, then indeed, KVL still holds within a varying magnetic field or with high frequency sources since it is dependent on a conservation of energy argument. It ultimately boils down to the model being insufficient to explain everything that is happening in the circuit rather than a problem with KVL.

This issue actually turned into quite a big discussion online which resulted in a very in-depth look at a series of definitions and experiments. A whole lot more can be found at the following places:
ElectroBOOM's Initial Assertion
Followup video
Relevant paper by MIT Professor John Belcher in response

In any case, sorry about the interruption to the question chain. Please carry on.

Thanks for the links! Always glad to see people still helping out with Science Olympiad after high school (assuming you did Science Olympiad in high school?)

Nydauron
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### Re: Circuit Lab B/C

UTF-8 U+6211 U+662F wrote:
MattChina wrote:
UTF-8 U+6211 U+662F wrote:

No, there are some cases where they don't apply. With KVL, it doesn't apply with a varying magnetic field, and with KCL, it doesn't apply when the voltage source has a very high frequency. Anyways, your turn!

Whoops...

Calculate the electric field strength 1 micrometer from a proton (e=1.6e-19 C).

If a proton is moving east at 300 m/s and experiences an acceleration of 2.6e10 m/s^2 south, what is the strength and direction of the B-field (the mass of a proton is 1.67e-27 kg)?

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UTF-8 U+6211 U+662F
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### Re: Circuit Lab B/C

Nydauron wrote:
UTF-8 U+6211 U+662F wrote:
MattChina wrote:
No, there are some cases where they don't apply. With KVL, it doesn't apply with a varying magnetic field, and with KCL, it doesn't apply when the voltage source has a very high frequency. Anyways, your turn!

Whoops...

Calculate the electric field strength 1 micrometer from a proton (e=1.6e-19 C).

If a proton is moving east at 300 m/s and experiences an acceleration of 2.6e10 m/s^2 south, what is the strength and direction of the B-field (the mass of a proton is 1.67e-27 kg)?

I probably should've given Coulomb's constant in the problem... But I think east and south are always orthogonal, no? Anyway, your turn!

Nydauron
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### Re: Circuit Lab B/C

UTF-8 U+6211 U+662F wrote:
Nydauron wrote:
UTF-8 U+6211 U+662F wrote:Whoops...

Calculate the electric field strength 1 micrometer from a proton (e=1.6e-19 C).

If a proton is moving east at 300 m/s and experiences an acceleration of 2.6e10 m/s^2 south, what is the strength and direction of the B-field (the mass of a proton is 1.67e-27 kg)?

I probably should've given Coulomb's constant in the problem... But I think east and south are always orthogonal, no? Anyway, your turn!

Yes you are definitely correct that east and south are orthogonal, but in the case of the Right Hand "Slap" Rule...(my Physics teacher was great )

...the angle is between the magnetic field vector and the velocity vector. Since you gave the force vector and the velocity vector, the magnetic field vector can be pointed where $\theta \in (0, \pi)$ . The vector could have been pointing almost west or almost east while also being slightly out of the page, but the magnitude of the magnetic field vector in both cases would be extremely large compared to when it is perpendicular to the velocity vector. Plus, it makes the math a LOT simpler if we assume the magnetic field vector just comes straight out of the page. Mathematically, the force vector is merely just the cross product of the magnetic field and the velocity vector. Either way, I digress...onto the next question!

Oh no! Dr. Doom has just finished building his capacitor! When designing the build he decided to make the plates have an area of 10 m^2 separated by 1 mm. As the dielectric, he used strontium titanate (k = 310). Dr. Doom plans on using his battery with an EMF = 20kV connected to a set of 20 parallel 100 Mohm resistors in series to charge the capacitor.
1) How long will it take to "fully" charge the capacitor?
2) How much charge will the capacitor hold when it reaches maximum voltage?
3) How much energy is stored in the charged capacitor? How much energy is lost during the process of charging the capcitor?
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