Lab Section
- Theory
When charged particles flow through a given magnetic field, force is exerted on them. Likewise, charged particles that are in motion induce magnetic fields around the conductor in which they flow. Biot-Savart law is stated by the formula shown below;
dB=μo IdL*r4πr3
In the formula, µo represents the permeability of free space, r represents vector displacement pointing from the section of the wire carrying current to the point whose magnetic field is being determined, and dl refers to a vector quantity with the value equal to the length of the segment of current. Biot-Savart law also outlines that magnetic field is proportional to the current causing it. The right hand rule is used to determine the direction of magnetic field. In order to determine the magnitude of magnetic field around a current-carrying loop, Biot-Savart law can be used as shown below;
Bz=(μoI2)(R2R2+Z232)
In this case, z is the position on the axis of the loop carrying current, I represent the current in the loop, and B (z) represents the magnetic field at position z. Since this experiment uses a coil of many turns, the principle of superposition is used. This principle suggests that the net magnetic field induced by all turns of the coil is equal to the sum of the magnetic field caused by each loop of the coil. Therefore, the formula below is used to determine the magnetic field along the axis of the coil.
Bz=(μoNI2)(R2R2+Z232)
In this case, N is the number of turns in the coil. If the distance along the axis of the coil (z) is zero, the formula below is used;
Bz=(μoNI2R)
- Data table
Data obtained from the experiment is shown in the tables below;
Field coil radius, R=0.105m Number of turns in field coil, N=200
The graphs obtained from the experiment are shown below
Figure 1: graph of B field against current, I
Figure 2: graph of expected B field against current, I
Figure 3: Graph of B field (T) against position on axis (Z)
- Questions
Question 1
The graph in part 1 shows that the magnetic field strength is proportional to the current in the coil as expected. The proportionality is explained by the fact that the graph has a curve that rises from left to right. In this case, as the amount of current increases, the magnitude of magnetic field strength also increases.
Question 2
The slope of the graph of magnetic field strength against current and that of expected magnetic field strength against current is 4.439 and 4.785 respectively. In this case, the difference between the two values is 0.346. This is a difference of 7.94%. The difference between the two slopes is not significant. Therefore, the slope of magnetic field strength against current is consistent with the expected value.
Question 3
Given that the net magnetic field is zero at the center of the two concentric loops, it means that their magnetic field strength cancel out at the center. This means that the current in the two loops flow in opposite directions. The magnitude and direction of the current in the outer loop can be determined as shown below;
dB=μo IdL*r4πr3
Taking the radius of the outer circle to be 2R and that of the inner circle to be R, we can equate the formulas for magnetic field strength of the two as shown;
μo IdL*2R4π(2R)3=μo 1dL*R4πr3
μo IdL*2R=μo 1dL*R4π8R34πr3
I*=μo 1dL*R4π8R3dL*μo *2R*4πR3
Current (I) = 4A. Therefore, the current of the outer loop is 4A and its direction is anticlockwise.
Question 4
The magnetic field strength decreases as the distance along the axis from the center of the loop increases. This is illustrated in graph 3 since the curve slopes from left to right. This implies that as the position on the axis increases, the magnetic field strength decreases.
- Conclusions
This experiment was performed in two steps: part 1 and part 2. In part 1, the students measured the magnetic field strength at the center of a current-carrying coil and how it varied with variation in the amount of current. The students then used the results to verify the predictions stated by Biot-Savart law. In part two, the students measured the magnetic field strength along the axis of a current-carrying coil. In this case, the students first placed the magnetic sensor at the center of the loop and then recorded the magnetic field strength measured. The measurements were then taken at an interval of 5cm. the students also calculated the expected value of magnetic field strength at each point in order to compare with the measured values.
The results obtained from the experiment were found to differ insignificantly from the expected results. Therefore, the experiment was performed accurately, and the procedure was followed accordingly. However, errors occurred and these contributed to the discrepancies observed. Errors in this experiment were due to the limited capabilities of the instruments used to take accurate measurements. In addition, errors were due to some factors inherent to the coil that could have caused interference with the flow of current in the coil.
