Finding Magnetic Field in a Square Coil with Tangent Galvanometer

[Soshamim]

Hey, I was wondering how would you find the value of the magnetic field inside a square coil? My books talk about finding the value of the mag. field at the center of a circular coil and everytime I search google for galvanometers made with square loops, I only find information on circular loops.

In case you're wondering what my class is doing, our teacher wants us to make a lab that he can use for his future students, so my partner and I chose to make a lab that determines the relationship between the current and the angle the compass needle makes with the vertical plane of the coil.

Thanks in advance.

-Syed

 

[OlderDan]

Hey, I was wondering how would you find the value of the magnetic field inside a square coil? My books talk about finding the value of the mag. field at the center of a circular coil and everytime I search google for galvanometers made with square loops, I only find information on circular loops.

In case you're wondering what my class is doing, our teacher wants us to make a lab that he can use for his future students, so my partner and I chose to make a lab that determines the relationship between the current and the angle the compass needle makes with the vertical plane of the coil.

Thanks in advance.

-Syed

I replied to your other post about this in the College thread. Here you have provided more information. You don't need to calculate the field produced by the rectangular coil. You need to calculate the torque on the coil because it is carrying an electric current and it is in a magnetic field produced by a pemanent magnet. Here is a nice graphic of rthe workings of such a device

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/galvan.html

To find the relevant mathematics, do a search for a magnetic dipole. The calculation is easiest for a rectangular coil, but can be generalized to any shape. For example

http://www.pa.msu.edu/courses/2000spring/PHY232/lectures/magmaterials/dipoles.html

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magmom.html

 

[Andrew Mason]

Hey, I was wondering how would you find the value of the magnetic field inside a square coil? My books talk about finding the value of the mag. field at the center of a circular coil and everytime I search google for galvanometers made with square loops, I only find information on circular loops.

In case you're wondering what my class is doing, our teacher wants us to make a lab that he can use for his future students, so my partner and I chose to make a lab that determines the relationship between the current and the angle the compass needle makes with the vertical plane of the coil.

If this is a tangent galvanometer, the compass needle is in the geometric centre of the loop. It aligns with the vector sum of the coil's and Earth's magnetic field. So all you have to do is relate the magnetic field in the centre of a square coil to the current. You have to use the Biot-Savart law for that.

It is not quite 4 times the field a distance L/2 from a long conducting wire since the sides of the loop are not arbitrarily long. But that is probably a fair approximation.

$$B = 4\frac{\mu_0I}{2\pi d} = \frac{4\mu_0I}{\pi L}$$ where d = L/2[/tex]

To get the exact value, you have to do a Biot-Savart integration over the length of the 4 sides.

AM

 

[Soshamim]

Hey AM, yes this is a tangent galvanometer. The equation you gave me, does that take into account the number of turns in the coil?

 

[OlderDan]

Hey AM, yes this is a tangent galvanometer. The equation you gave me, does that take into account the number of turns in the coil?

Sorry, I totally missed the "tangent" business in my earlier reply. AM's equation does not include multiple turns. It assumes one wire carrying a current I. If you have multiple turns, each carrying a current I, then effectively you have N times the current of a single wire, so you would need to multiply by N.

I thought you were trying for find the field everywhere within your rectangular coil. Now I see you really only need it at the center. AM's equation is an approximation because it is the field from four wires of infinite length. Your wires are not infinite, and as he said you would need to do a calculation using the law of Biot-Savart to get the correct result for shorter wires. I have found one source that gives the result of that calculation for a wire of finite length at an arbitrary point in the vicinity of the wire. You can use the equation to solve your problem at the center of the coil, and if you want to you can explore the variation in the field as you move a bit away from the center. You will find the equation here:


http://www.westbay.ndirect.co.uk/field.htm

Click on the link titled

"Magnetic Field due to a Current in a Wire". Make sure you use the equation for the short wire, Bsw.

Here is another useful link

http://www.magson.de/technology/tech41.html

It gives the fields anywhere along the axis of a circular or rectangular coil. It also gives the fields for circular or square double coils (Helmholtz coils). As you can see from the pictures here

http://physics.kenyon.edu/EarlyAppa...angent_Galvanometer/Tangent_Galvanometer.html

many of these devices use double coils.

 

[Andrew Mason]

Hey AM, yes this is a tangent galvanometer. The equation you gave me, does that take into account the number of turns in the coil?

As Dan pointed out, this is for a single wire loop. Just multiply by n = the number of turns. Follow the first link that Dan provided to work out the field of each side of the loop. Using the principle of superposition, the total field is the vector sum of the fields of all 4 wire segments.

AM

 

[Soshamim]

sup Andrew and Dan, I just wanted to say thank you for all the help, the links were pretty useful and explanatory. Sorry for not responding earlier though as I've been busy with studying for finals lately