Introduction: Current in a wire produces a magnetic field around a wire. Using the right-hand rule convention, the shape of the magnetic field and current can be determined (concentric circles of field). This was discovered by Oersted in 1820. The field decreases in strength as you move away from the wire falling off as 1/r2. Using the right hand rule, you are able to prove that from a loop of wire, that all of the sections of the wire contribute to a field inside the loop that all point in the same direction. By symmetry, in the centre of the loop, the field would not be able to point in any other direction.
A compass needle is a magnetic dipole. It will always feel torque in a magnetic field; it will be able to align itself with the direction of the field. A dipole will however experience a net force at a different direction if there is a field gradient. If you were to float a magnetized needle on a pool of liquid, a gradient to the earth’s magnetic field would not be detected. The needle will not drift, but will just rotate. For this experiment, we can assume that the earth’s magnetic field is uniform at one spot on earth. There is a vertical and horizontal component to the earth’s magnetic field. At the north pole end, the compass would point down into the earth. Around 35% of the total magnetic field is horizontal (parallel to the earth’s surface) at our latitude.
For this lab, a vector calculation is used to prove that the magnetic field produced by a current in a wire is directly proportional to the current in the wire. We also demonstrate that the number of loops is directly proportional to the field inside a series of the loops. From these results the fields from the geometry and the current can be calculated. Using Ampere’s law, the strength of the Earth’s magnetic field and can be calculated to then be compared to literature values.
Purpose: The purpose of this lab is to calculate of the magnetic field of a current loop and measuring the Earth’s magnetic field by comparing it to literature values. Loops
The object of the experiments is to investigate some of the parameters that affect the magnetic field inside a loop of wire (BL). Power Supply
Make sure that you have an integer set of loop in your apparatus. Starting with 5 loops. We set up a system so the compass was at 45o to the plane of the loop. We did this by aligning the 45o and 225o directions of the compass scale with the line drawn on the centre platform. Next, we left the compass in the position on the platform, and rotated the entire loop from (with the compass) until the end (red end) of the needle is at the 0o N mark on the scale. That aligned the Earth’s field with the N on the scale, which is at a 135o to the field that is about to be generated. We then connected the power supply to the loops of wire. We then connected the supply serially through an ammeter to the loops. For Data Set I, the first experiment is to determine the relationship between current and the magnetic field produced by the loops. We turned the current up until we shifted the compass from North by 30o. For Data Set II and III, we repeated the steps for Data Set I twice more with 4 and 3 loops each time (for a total of three sets of data).
Data Analysis: [UNCERTAINTY +/- 2 or 3o]
Data Set I
5 loops| | | | | |
Angle (degrees)| I1| I2| I3| I Avg| Bl/BE|
0| 0| 0| 0| 0| 0|
30| 0.21| 0.22| 0.21| 0.213333333| 0.51763|
45| 0.28| 0.29| 0.29| 0.286666667| 0.7071|
60| 0.37| 0.37| 0.37| 0.37| 0.89657|
90| 0.6| 0.57| 0.59| 0.586666667| 1.41421|
110| 0.92| 0.87| 0.93| 0.906666667| 2.2235|
Data Set I Conclusion: As the current increases, the BL/BE angle ratio increases. The number of loops was 5, meaning that the slope/gradient would increase quickly; it...