# Need help in finding error in calculation to find Earth's magnetic field strength using Galvanometer

I am working on a experiment on finding the Earth's magnetic field strength. Using a Galvanometer and a constant power source of 5.1V and slowly adjusting the resistance, I was able to find the changes in angle in relation to the changes of current.

https://en.wikipedia.org/wiki/Galvanometer#Theory

$$\frac{\mu_0nI}{2r}=B_H\tan\theta$$

Then I used the equation to find the $$B_H$$, the horizontal component BH of the Earth's magnetic field.

However, my calculation shows my $$B_H$$ is 5.62E-04, while the actual $$B_H$$ is 5.03E-05. There is a difference of factor of 10!!!

• Hard to say what it might be without actually being there and going over the setup and calculations in detail. Since, as you noted, the calculation is off by nearly a factor of 10 so I would start off by checking to make sure that there wasn't an accident or error in which a factor of 10 crept in. For example, N=50 turns but the spreadsheet says that the total coil is 500 turns. Sure that a partial and not total coil was used? Also, the magnetic inclination is a steep 70˚ in Denmark, so the field is far from horizontal there. Sure that the experiment was properly set up for that?
– user93237
Sep 3, 2018 at 23:31
• There are 2 settings on the device, 1 setting to turn on all 500 turns and 1 setting to turn on only 50 turns. I use the setting for 50 turns. If 500 turns is used in the calculation, the difference will be a factor of 100 instead of 10. μ (N/2r) I = Bh tan Bh = μ (N/2r) (1/slope) How did you get the 70˚ for the magnetic inclination? What would be a reasonable value?
– Tom
Sep 4, 2018 at 6:14
• I found out about the 70˚. Ignore that question:-)
– Tom
Sep 4, 2018 at 6:23
• There is possibly something inconsistent with your data. In your tabulated data to what does the resistance refer? Was it the resistance of a resistor in series with the tangent galvanometer? Was the supply voltage constant at $5.1\,\rm V$? If the answers are all yes then the extra resistance in the circuit (the resistance of the tangent galvanometer) varied from over $100 \Omega$ for low currents to below $30 \Omega$ for the higher currents. Sep 4, 2018 at 7:51
• I will look into the volts/resistance/current issue by doing another experiment, if possible. I will take some photos next time so it is easier to double check the data.
– Tom
Sep 4, 2018 at 10:40

It seems to be the case that such a galvanometer is most accurate at around $\theta=\pi/4=45^\circ$. The optimum current for this defection (assuming the correct $B_h$ is present is given by
$I=\frac{2rB_h}{\mu_0n}\approx1.2amps$
I wonder if it is correct to operate your particular device, as you seem to have done, with a deflection under $\theta=\pi/20=10^\circ$ and at currents an order of magnitude less than 1.2amps? (Note that incorporating more turns would also reduce the optimum current).