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Author Topic:   Magnetic Field From DC Current

jimh posted 04-04-2015 12:18 PM ET (US)
If a DC current flows in a straight wire conductor, what is the strength of the magnetic field at 90-degrees to the conductor? The strength varies with the distance and current, so please tell me in terms of the distance R and the current I.
I think the strength may be described by
β = μ x I / (2 x pi x R) where R is in meters, I is in amperes, and μ = (4 x pi x 10^-7)

For I = 1-Ampere and R = 1-Meter the field is thus β = 2 x 10^-7
Is that right? Perhaps we have a Physicist (or perhaps a retired Physicist) that could comment on this. What units?
Compare at:
https://www.pa.msu.edu/courses/1997spring/PHY232/lectures/ampereslaw/ wire.html
saumon posted 04-04-2015 04:40 PM ET (US)
Nicely explained in this Power Point presentation. The formula is on page 4, with a example on page 5.
B=kI/r
(same as yours, where k=u/2 x pi)
B= magnetic field strength (in Tesla)
k= permeability of free space constant (2x10 exp -7)
I= current (in Amps)
r= distance from wire (in meter).
The remaining of the presentation show calculations is for loops and coils.
(Please forgive my bad English)
Interestingly, I would have thought, intuitively, that it would be inversely proportional to the square of the distance, as are a lot of forces, but it's not.
jimh posted 04-05-2015 10:01 AM ET (US)
Many thanks for confirming my calculations.
The reason for this inquiry is to assess the strength of the magnetic field that might radiate from a conductor when a DC current flows through it, and then compare that field to the strength of the Earth's magnetic field.
For the strength of the Earth's magnetic field, I found a citation in a Wikipedia article:
http://en.wikipedia.org/wiki/Orders_of_magnitude_(magnetic_field)
That article mentions the Earth Magnetic Field strength as being about
30 to 60 x 10^-6 Tesla (30 to 60 microTesla)
depending on latitude. Any comments on that value? Maybe we need a Geo-Physcist to join us.
Hoosier posted 04-05-2015 06:07 PM ET (US)
I'm assuming [the reason for this inquiry] has to do with magnetic interference with the boat's magnetic compass caused by the fields created by the wiring of the boat's electronics.
So,
B=kI/R
B= (2x10^-7)(1)/1
B= 2x10^-7
Note this from the Wikipedia citation:
10^−5 31 µT strength of Earth's magnetic field at 0° latitude
58 µT strength of Earth's magnetic field at 50° latitude
So, if the earth's magnetic field is~ 4x10^-6, that makes it 2x100 times (200) stronger the field generated by the current in the conductor if the device is drawing 1 Amp dc and is 1 meter from the compass. Interestingly most manufacturers say to put their stuff at least 1-meter from your compass. A pulse sonar may have a peak power through the wire that boosts the field up, but only for a short pulse, too short for the compass to respond to it. An FM (aka CHIRP) sonar will have a peak power well below that. The issue with Boston Whaler consoles is it's really hard to get 1-meter from the compass and still be in/on the console.
Even then since it's a dc current one can assume that it's steady-state and one can make a deviation correction for any induced compass errors by checking compass heading while running a Range and noting the delta.
Going back to the Wikipedia citation you will have a lot more problems if you put your remote speaker or loud hailer next the compass. If you do that the compass will always point to the speaker's magnet.
jimh posted 04-06-2015 06:46 AM ET (US)
The reason the equation for field strength is not proportional to the inverse-square may be that the equation only computes the magnetic field. The electric field is probably also in the same proportion, so maybe the net electro-magnetic field ends up as the inverse-square--but that's just a guess with only one cup of coffee this morning.
jimh posted 04-06-2015 06:48 AM ET (US)
Re the reason for the discussion: the reason for the discussion was mentioned in my second post:

quote:
The reason for this inquiry is to assess the strength of the magnetic field that might radiate from a conductor when a DC current flows through it, and then compare that field to the strength of the Earth's magnetic field.
jimh posted 04-13-2015 09:02 AM ET (US)
Let us assume the conditions mentioned by HOOSIER in his earlier article in the thread, that is, the magnetic field from a conductor with 1-Ampere of current located 1-meter from the compass has an intensity that is only 1/200th the intensity of the magnetic field of the Earth. We now look at how the compass might be affected by this field.
The worst case for the local magnetic field affecting the compass would occur when the local field is at 90-degrees to the Earth field. We can construct a vector diagram. The vectors are at 90-degrees. The magnitude of the vectors are 1 for the local field and 200 for the Earth field. The angle the compass will be deflected away from the Earth field by the local field is found from the resultant vector. This ought to be
Angle of Compass Deflection = ArcTan(1/200) = 0.286-degrees
Any comments on this analysis?
jimh posted 04-13-2015 12:22 PM ET (US)
If the 1-Ampere current flowing in a conductor that was 1-meter away from the compass were paired with a current of equal magnitude flowing in the opposite direction, the magnetic field of the two conductors would tend to cancel. The cancellation might not be perfect, but it seems reasonable to assume the cancellation ought to remove about 90-percent of the field. The remaining field would therefore be only 1/10th as strong. If we assume those conditions, the local field would then be only 1/2000th as strong as the Earth field. The deflection would then be on the order of
ArcTan(1/2000) = 0.03-degrees
Hoosier posted 04-13-2015 03:20 PM ET (US)
Someplace in the CW archives there is a thread about magnetic compass accuracy and card damping. Since Jim's calculations are always correct, and even a high end yacht compass can't measure to 0.286 degree precision, this isn't something to worry about. Placing other magnetic devices, like speakers, near a magnetic compass will cause a lot more problems; even putting a pair of pliers on top of the console near the compass will mess it up.
jimh posted 04-14-2015 12:42 AM ET (US)
The loudspeaker is a problem for two reasons:
--there is a really strong magnet in the loudspeaker
--the strength of the magnetic field is sufficient to actually move the physical speaker cone back and forth by a deflection of some travel, which suggests that the forces are rather strong. That sort of movement seems like it would need a lot more force than needed to deflect a very sensitive compass card spinning on a jeweled bearing. The speaker is absorbing several Watts of electrical power. This also suggests very strong field.
saumon posted 04-14-2015 01:15 PM ET (US)
About the effects of magnet: after the installation of a Garmin GPSMAP 740S on the top of the console beside a Ritchie Explorer compass, it went crazy. It turns out it was the very tiny magnet holding the door for the sd card closed that caused this. Moved the chartplotter to the other side of the compass, so the magnet was 18-inches instead of 6-inches away from the compass, and the problem was solved.

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Author	Topic: Magnetic Field From DC Current
jimh	posted 04-04-2015 12:18 PM ET (US) If a DC current flows in a straight wire conductor, what is the strength of the magnetic field at 90-degrees to the conductor? The strength varies with the distance and current, so please tell me in terms of the distance R and the current I. I think the strength may be described by β = μ x I / (2 x pi x R) where R is in meters, I is in amperes, and μ = (4 x pi x 10^-7) For I = 1-Ampere and R = 1-Meter the field is thus β = 2 x 10^-7 Is that right? Perhaps we have a Physicist (or perhaps a retired Physicist) that could comment on this. What units? Compare at: https://www.pa.msu.edu/courses/1997spring/PHY232/lectures/ampereslaw/ wire.html
saumon	posted 04-04-2015 04:40 PM ET (US) Nicely explained in this Power Point presentation. The formula is on page 4, with a example on page 5. B=kI/r (same as yours, where k=u/2 x pi) B= magnetic field strength (in Tesla) k= permeability of free space constant (2x10 exp -7) I= current (in Amps) r= distance from wire (in meter). The remaining of the presentation show calculations is for loops and coils. (Please forgive my bad English) Interestingly, I would have thought, intuitively, that it would be inversely proportional to the square of the distance, as are a lot of forces, but it's not.
jimh	posted 04-05-2015 10:01 AM ET (US) Many thanks for confirming my calculations. The reason for this inquiry is to assess the strength of the magnetic field that might radiate from a conductor when a DC current flows through it, and then compare that field to the strength of the Earth's magnetic field. For the strength of the Earth's magnetic field, I found a citation in a Wikipedia article: http://en.wikipedia.org/wiki/Orders_of_magnitude_(magnetic_field) That article mentions the Earth Magnetic Field strength as being about 30 to 60 x 10^-6 Tesla (30 to 60 microTesla) depending on latitude. Any comments on that value? Maybe we need a Geo-Physcist to join us.
Hoosier	posted 04-05-2015 06:07 PM ET (US) I'm assuming [the reason for this inquiry] has to do with magnetic interference with the boat's magnetic compass caused by the fields created by the wiring of the boat's electronics. So, B=kI/R B= (2x10^-7)(1)/1 B= 2x10^-7 Note this from the Wikipedia citation: 10^−5 31 µT strength of Earth's magnetic field at 0° latitude 58 µT strength of Earth's magnetic field at 50° latitude So, if the earth's magnetic field is~ 4x10^-6, that makes it 2x100 times (200) stronger the field generated by the current in the conductor if the device is drawing 1 Amp dc and is 1 meter from the compass. Interestingly most manufacturers say to put their stuff at least 1-meter from your compass. A pulse sonar may have a peak power through the wire that boosts the field up, but only for a short pulse, too short for the compass to respond to it. An FM (aka CHIRP) sonar will have a peak power well below that. The issue with Boston Whaler consoles is it's really hard to get 1-meter from the compass and still be in/on the console. Even then since it's a dc current one can assume that it's steady-state and one can make a deviation correction for any induced compass errors by checking compass heading while running a Range and noting the delta. Going back to the Wikipedia citation you will have a lot more problems if you put your remote speaker or loud hailer next the compass. If you do that the compass will always point to the speaker's magnet.
jimh	posted 04-06-2015 06:46 AM ET (US) The reason the equation for field strength is not proportional to the inverse-square may be that the equation only computes the magnetic field. The electric field is probably also in the same proportion, so maybe the net electro-magnetic field ends up as the inverse-square--but that's just a guess with only one cup of coffee this morning.
jimh	posted 04-06-2015 06:48 AM ET (US) Re the reason for the discussion: the reason for the discussion was mentioned in my second post: quote: The reason for this inquiry is to assess the strength of the magnetic field that might radiate from a conductor when a DC current flows through it, and then compare that field to the strength of the Earth's magnetic field.
jimh	posted 04-13-2015 09:02 AM ET (US) Let us assume the conditions mentioned by HOOSIER in his earlier article in the thread, that is, the magnetic field from a conductor with 1-Ampere of current located 1-meter from the compass has an intensity that is only 1/200th the intensity of the magnetic field of the Earth. We now look at how the compass might be affected by this field. The worst case for the local magnetic field affecting the compass would occur when the local field is at 90-degrees to the Earth field. We can construct a vector diagram. The vectors are at 90-degrees. The magnitude of the vectors are 1 for the local field and 200 for the Earth field. The angle the compass will be deflected away from the Earth field by the local field is found from the resultant vector. This ought to be Angle of Compass Deflection = ArcTan(1/200) = 0.286-degrees Any comments on this analysis?
jimh	posted 04-13-2015 12:22 PM ET (US) If the 1-Ampere current flowing in a conductor that was 1-meter away from the compass were paired with a current of equal magnitude flowing in the opposite direction, the magnetic field of the two conductors would tend to cancel. The cancellation might not be perfect, but it seems reasonable to assume the cancellation ought to remove about 90-percent of the field. The remaining field would therefore be only 1/10th as strong. If we assume those conditions, the local field would then be only 1/2000th as strong as the Earth field. The deflection would then be on the order of ArcTan(1/2000) = 0.03-degrees
Hoosier	posted 04-13-2015 03:20 PM ET (US) Someplace in the CW archives there is a thread about magnetic compass accuracy and card damping. Since Jim's calculations are always correct, and even a high end yacht compass can't measure to 0.286 degree precision, this isn't something to worry about. Placing other magnetic devices, like speakers, near a magnetic compass will cause a lot more problems; even putting a pair of pliers on top of the console near the compass will mess it up.
jimh	posted 04-14-2015 12:42 AM ET (US) The loudspeaker is a problem for two reasons: --there is a really strong magnet in the loudspeaker --the strength of the magnetic field is sufficient to actually move the physical speaker cone back and forth by a deflection of some travel, which suggests that the forces are rather strong. That sort of movement seems like it would need a lot more force than needed to deflect a very sensitive compass card spinning on a jeweled bearing. The speaker is absorbing several Watts of electrical power. This also suggests very strong field.
saumon	posted 04-14-2015 01:15 PM ET (US) About the effects of magnet: after the installation of a Garmin GPSMAP 740S on the top of the console beside a Ritchie Explorer compass, it went crazy. It turns out it was the very tiny magnet holding the door for the sd card closed that caused this. Moved the chartplotter to the other side of the compass, so the magnet was 18-inches instead of 6-inches away from the compass, and the problem was solved.