Biot-Savart Law

Magnetic Field of the Earth

In this experiment, we calculate the magnetic field of the earth using a compass and a magnetic field created a coil with current passing though it.

We first we obtained wire that has been looped around many times around a cardboard circle with a stand for a compass to be placed inside. The compass was placed and the whole wire-compass setup was rotated until the compass was "zeroed" at north. Angles were to be measured, therefore it is easier to start at zero though we could have also measured the angle displacement (final-initial).

Here we see the coils in their zeroed form. The ends of the coils were hooked up to a power supply via alligator clips. We noted on the cardboard that the diameter was measured as 4.7 cm or D =  0.047 m. Also noted on the cardboard were the number of turns, N = 39 turns, or loops of the wire.

Took a multimeter to measure the current going through the coil. We took this measurement as well as the angle displacement on the compass.

Here we see the data for 3 trials. We divided the magnetic field by the tangent of the angle displacement, as shown above, for each trial on the data. The calculation for the first trial is shown above. However, our data was 200% above the actual value, which is 2E-5. We looked through our data and finally realized that the diameter of the coil does not really look like 47 cm at all. The diameter recorded on the cardboard was incorrect!

We measured the diameter of the coil to be 14.7 cm. We recorded one more point at 32 mA for good measure and recalculated everything using the formula shown above.

We used an Excel spreadsheet for our calculations. We made sure to convert our measured degrees to radians before calculating. We saw that our new values were much closer than in the previous data set. We calculated an average and then a percent error. Although the percent error was a bit higher than what we desired, there was a huge uncertainty in our measurements of loop diameter, current measurement, and the largest, angle measurement.

Magnetic Field at Center of Solenoid

Magnetic Field at Center of Square Loop with Current