Magnetic Fields

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Magnetic Fields
Introduction:
This lab was completed to investigate and map the magnetic field pattern of a single straight conductor by comparing it with the earth’s magnetic field. Quantitatively, the purpose of this lab was to determine the horizontal component of the earth’s magnetic field. Magnetic field and electric currents are naturally closely related because anytime a current runs through a wire, a magnetic field around the wire is created. These magnetic fields can be expressed in terms of both magnitude and direction and are, therefore, vector fields. The magnitude of a magnetic field from a straight wire can be determine with the following equation: B = (μ0I)/(2πy),

where B is the magnitude in units Tesla, μ0 is the permeability of free space with a value of 4π×10-7 Tm/A, I is the current running through the wire in amperes, and y is the perpendicular distance in meters away from the wire to the point where the magnetic field is being measured. Distance away from the wire and the strength of the magnetic field are inversely related. That’s is, as the distance increases, the magnetic field decreases. Additionally, although a Tesla is the standard unit of measurement for magnetic fields, a Tesla is a rather large unit of magnetic field. Therefore, magnetic fields are also commonly measured in “Gauss,” which are equal to 10-4 Tesla.

In order to determine the direction of the magnetic field around a wire, an easy trick to use is the right hand rule. Simply place your right thumb along the wire to point in the same direction of the current. Curl your fingers around the wire. The resulting direction that your fingers circle around and point corresponds to the direction of the magnetic field. A schematic of the right hand rule (left side) and current and magnetic field direction (right side) is seen below (Figure 1).

Figure 1: right hand rule (left) and current/magnetic field direction (right)
In this lab, a magnetic compass is used to measure the magnetic field produced by the electrical current flowing through the conductor (BI) by comparing the value to the horizontal component of the earth’s magnetic field (BHoriz Earth). At the initial position, the compass points directly at the conductor/wire with no current running through the wire. Here, BI is perpendicular to BHoriz Earth because BI is always tangent to a circle centered on the conductor. When the current flows through the conductor, and I is a non-zero value, the compass needle moves to align its arrow with the total magnetic field that is produced: Btotal = BI + BHoriz Earth. Since the compass is in a position so that BI is perpendicular to BHoriz Earth, the needle points at an angle δ in relation to BHoriz Earth. This relationship can be expressed mathematically by: tan δ = BI / BHoriz Earth.

Including the general equation for the strength of a magnetic field, the equation can be written as: tan δ = (μ0I) / (2πyBHoriz Earth).
This relationship and orientation of the compass, BI, BHoriz Earth, the angle δ, and current can be seen in Figure 2 below.

Figure 2: Magnetic field setup

Procedure:
A couple of special precautions must be considered before beginning the lab. First, the power supply may not be set to run a current any higher than 8 Amps, although much lower (around 5) is probably recommended. Second, there may be significant variation in ambient magnetic field from table to table throughout the room, especially at tables made of steel and considering that research is conducted in the same building.

In the set up of this lab, a long straight conductor is connected to an ammeter and a power supply. A horizontal clear plastic plate is attached to allow compass measurements to be done near the center of the conductor. First, the compass was positioned so that the compass needle pointed directly towards the wire, that is, so that BI and BHoriz Earth were perpendicular to each other once current ran...
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