Experiment 3 - Magnetic Fields Of Coils 4bg4x

Abstract: The purpose of this experiment was to determine the effect of changing coil separation on magnetic fields created by solenoids. Due to an error in the interpretation of the procedure the two magnetic fields were oriented in an incorrect fashion resulting in destructive interference between the two magnetic fields rather than constructive interference as seen in Helmholtz coils. However it was found that increasing the distance between the coils would reduce the interference and result in a stronger magnetic field at each coil. Decreasing the distance between the coils would result in more interference and therefore a lower maximum magnetic field strength. Each magnetic field was equal in magnitude but opposite in direction. This experiment proved that magnetic fields not aligned correctly in series will result in an interference of magnetic fields. Introduction: This experiment involves the measurement of magnetic field as various locations along an axis through one or more solenoid coils. The magnetic field at a particular point relative to the centre of the coil can be determined using Equation 1. The magnetic field at a point where multiple coils are present can be determined through finding the sum of all the magnetic fields. Equation 1: Magnetic field along the perpendicular axis through the center of a coil B

o NIR2



2 x2  R2



3 2

Where B is the magnetic field (T), µo is the permeability of free space (4π*10-7Tm/A), N is the number of turns in the coil, I is the current moving through the coil (A), R is the radius of the coil (m), and x is the position along the axis (m). Procedure: The experiment was performed as per the experiment “Magnetic Fields of Coils” found in the Introduction to Experimental Physics lab manual.

Data and Analysis:

Magnetic Field Strength (T)

2.50E-03

2.00E-03

1.50E-03

1.00E-03

5.00E-04

0.00E+00 -2.50E-01 -2.00E-01 -1.50E-01 -1.00E-01 -5.00E-02 0.00E+00 5.00E-02 1.00E-01 1.50E-01

Position (m)

Figure 1: Magnetic field strength along the perpendicular axis to the centre of a single solenoid. In this setup the wire has a DC voltage of 15V, the radius of the coil is 0.0975m and the coil has 500 turns. The maximum magnetic field is seen at approximately the centre of the coil with a strength of 2.33*10-3 T.

Magnetic Field Strength (mT)

2.5 y = (2.7963 ± 0.05)x + 0.0253 R² = 1

2

1.5

1

0.5

0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Current (A)

Figure 2: Magnetic field strength at the centre of a solenoid with varying current. The radius of the coil is 0.0975m and the coil has 500 turns. Using Equation 1 and the slope of the graph the experimental permeability of free space µo can be calculated to be 1.091*10-6Tm/A. This is slightly lower than the theoretical value of 4π*10-7Tm/A.

Magnetic Field Strength (T)

1.50E-03 1.00E-03 5.00E-04

0.00E+00 -3.00E-01-2.50E-01-2.00E-01-1.50E-01-1.00E-01-5.00E-020.00E+005.00E-021.00E-011.50E-012.00E-01 -5.00E-04 -1.00E-03

Position (m) Run 1

Run 2

Run 3

Figure 3: Magnetic field strength along the perpendicular axis to the centre of two solenoids with various distances between them. In this setup the coils are connected in series, the wire has a current of 0.421A, the radius of each coil is 0.0975m and each has 500 turns. The coils are located in Run 1 at a distance apart equal to the radius of one coil. In Run 2 the coils are located 1.5 times the radius apart and in Run 3 the coils are located 0.5 times the radius apart. The theoretic maximum magnetic field strength for Run 1 is 1.8367*10-3T, for Run 2 is 1.588*10-3 T, and for Run 3 is 2.327*10-3. Separation of coils that were connected in series increased the maximum electric field strength at each coil. This was due to the decreased amount of interference between the magnetic fields created by the two coils. Discussion and Conclusion: In this experiment it was proven that oppositely oriented solenoids produce magnetic fields that will cancel each other in the centre of the space between them. Increasing the distance between the coils will decrease this interference. Due to a misinterpretation the true purpose of this experiment, to find the effect of the magnetic fields of solenoids in series was not determined. To do this, tests where the magnetic fields of the solenoids are oriented in the same direction must be performed.

Appendix: Calculation of experimental µo for a single coil: 𝐵=

𝜇𝑜 𝑁𝐼𝑅 2 3

2(𝑥 2 + 𝑅 2 )2 𝜇𝑜 𝑁𝐼 𝐵= 2𝑅 2𝐵𝑅 𝜇𝑜 = 𝐼𝑁 2(2.7963 ∗ 10−3 )(0.0975) 𝜇𝑜 = 500 𝜇𝑜 = 1.091 ∗ 10−6 𝑇𝑚/𝐴 Sample calculation for theoretical magnetic field: 𝜇𝑜 𝑁𝐼𝑅 2 𝜇𝑜 𝑁𝐼𝑅 2 𝐵= 3+ 3 2 2 2 2 𝑑 𝑑 2 ([ 2 + 𝑥] + 𝑅 2 ) 2 ([ 2 − 𝑥] + 𝑅 2 ) 𝐵=

(4𝜋 ∗ 10−7 )(500)(0.421)(0.0975)2 2 ([

𝐵=

2

2

0.0975 2 2 + 0.04875] + (0.0975) )

(4𝜋 ∗ 10−7 )(500)(0.421)(0.0975)2 2 ([

3+

2

3+ 2

0.0975 2 2 + 0.04875] + (0.0975) )

(4𝜋 ∗ 10−7 )(500)(0.421)(0.0975)2 2 ([

2

3 2

0.0975 2 2 − 0.04875] + (0.0975) )

(4𝜋 ∗ 10−7 )(500)(0.421)(0.0975)2 2 ([

2

3 2

0.0975 2 2 − 0.04875] + (0.0975) )

𝐵 = 1.8367 ∗ 10−3 𝑇