Calculate magnetic field of earth Prac Test (1 Viewer)

[Mitchie_Narker]

At school this is the basis of our Practical Test, how would you go about finding the value of the earth's magnetic field ASAP. Here is the method we are given for test attachted!

Aim: To make measurements of the deflection of a compass needle caused by nearby current carrying wire, to allow a rough estimate of the strength of the Earth's magnetic field.

Theory: A magnetic compass needle aligns itself with the Earth's magnetic field. When a current carrying wire is placed, parallel to, and directly above the compass, the magnetic field interacts with the Earth's magnetic field to create a resultant field, the direction of which is shown by the direction of the compass needle.

When the switch in the circuit is closed the potential difference established causes a current flow through the straight length of wire. The magnetic field produced by the current carrying wire is perpendicular to the Earth's field and the two fields interact to create a resultant magnetic field with the direction of this field indicated by the compass needle. With appropriate theoretical considerations, measurement of the deflection of the needle for different currents can allow analysis to enable a caluclation of the strength of the Earths magnetic field.

How would you graph the results you get from the test - current and magnetic field force of wire which you calculate using the formula given in the files section.

 

[Drdusk]

Ok here is one method that comes to mind...
Since we are approximating the B field of the conductor to always be perpendicular to that of the Earths, we can construct right angled triangles with the x component being and the y component being . Now each time you test with a different current, you want to measure the angle it deflects from its original vertical position. Lets suppose with a current of I it deflects from the vertical.

Since our triangle is using the angle from the horizontal, we need . This is assuming the needle only deflects at an angle less than 90 degrees. Make sure that's the case, or you will need to tweak the line below..

Therefore:


Now we know that , at a distance d from the wire which you can measure! (NOTE: this is a standard formula you must know!)

So we get:




Just on a note, the reason the angle varies with current is because is a vector quantity. So mathematically this stretches out the vector, causing a change in angle.

Also good luck for you prac. Don't stress through it because I know prac tests can get pretty heated, you know the method, now just make sure you fully understand it and if you don't then I'm here to help.

 

[Mitchie_Narker]

Ok here is one method that comes to mind...
Since we are approximating the B field of the conductor to always be perpendicular to that of the Earths, we can construct right angled triangles with the x component being and the y component being . Now each time you test with a different current, you want to measure the angle it deflects from its original vertical position. Lets suppose with a current of I it deflects from the vertical.

Since our triangle is using the angle from the horizontal, we need . This is assuming the needle only deflects at an angle less than 90 degrees. Make sure that's the case, or you will need to tweak the line below..

Therefore:


Now we know that , where at a distance d from the wire which you can measure! (NOTE: this is a standard formula you must know!)

So we get:




Just on a note, the reason the angle varies with current is because is a vector quantity. So mathematically this stretches out the vector, causing a change in angle.

Also good luck for you prac. Don't stress through it because I know prac tests can get pretty heated, you know the method, now just make sure you fully understand it and if you don't then I'm here to help.

Hi the formula we use instead of yours now is shown in the file i attached how i calucate earth magnetic field using that formula instead thanks.

 

[Drdusk]

Hi the formula we use instead of yours now is shown in the file i attached how i calucate earth magnetic field using that formula instead thanks.

The formula you have given is a more general case, known as Biot-Savarts LAW. I didn't use it because I didn't think they would actually teach you it in high school. Alas I have updated my post with that formula...

 

[Mitchie_Narker]

The formula you have given is a more general case, known as Biot-Savarts LAW. I didn't use it because I didn't think they would actually teach you it in high school. Alas I have updated my post with that formula...

Also we have to graph the results i get from the prac - i can find distance of the wire and the magnetic field of the wire as well as current - how would i graph this. then from this i get the gradient and would that gradient be equal to the magnetic field of earth or something thanks - prac test is tomorrow. also what should the table look like thanks

 

[Drdusk]

Also we have to graph the results i get from the prac - i can find distance of the wire and the magnetic field of the wire as well as current - how would i graph this. then from this i get the gradient and would that gradient be equal to the magnetic field of earth or something thanks - prac test is tomorrow. also what should the table look like thanks

Ah I see, I expected this to be the case.
So we have:





So now what you want to do is keep d constant sketch a graph of
The gradient of this graph will be

Rearrange and make the subject.

In your table, have one column for current, and another for and another for

 

[Mitchie_Narker]

Ah I see, I expected this to be the case.
So we have:





So now what you want to do is keep d constant sketch a graph of
The gradient of this graph will be

Rearrange and make the subject.

Wait i still dont understand how to find earth magnetic field from the gradient and also when doing angle of deflection why is it tan theta for the graph and what does the table look like for the results thanks also which axis is current and which is tan theta

 

[Mitchie_Narker]

Wait i still dont understand how to find earth magnetic field from the gradient and also when doing angle of deflection why is it tan theta for the graph and what does the table look like for the results thanks

Ah I see, I expected this to be the case.
So we have:





So now what you want to do is keep d constant sketch a graph of
The gradient of this graph will be

Rearrange and make the subject.

In your table, have one column for current, and another for and another for

do i also put in the magnetic field of the wire for the table

 

[Drdusk]

Wait i still dont understand how to find earth magnetic field from the gradient and also when doing angle of deflection why is it tan theta for the graph and what does the table look like for the results thanks also which axis is current and which is tan theta

You get from rearranging the above equation

Its easy, just sub in your value for the gradient and all the other values into your calculator.

The x axis is and the y axis is current.

Its like a linear equation. y=mx. the 'x' in this case is , and the 'y' is current.

I have updated my previous post for the table.

 

[Drdusk]

do i also put in the magnetic field of the wire for the table

You can I guess, I don't really see it necessary because it's not directly contributing to the graph. As the table and graph are directly linked to each other.

You can ask your teacher if you want to put it in but imo I don't think you need to.

 

[Mitchie_Narker]

You can I guess, I don't really see it necessary because it's not directly contributing to the graph. As the table and graph are directly linked to each other.

You can ask your teacher if you want to put it in but imo I don't think you need to.

That makes so much sense now! I get it also last thing we have to calculate is the uncertainty in our answer - where do u think we would have to caluclate the uncertainty in and how do you do this. we havent been taught it yet. Also what do i title the table and how would u go about improving the validity, relibality and accuracy of the experiment thanks