Phys 221 - Lab 8_ Magnetic Force and Fields

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Illinois Institute Of Technology *

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221

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Apr 3, 2024

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RC Circuits 1 Introduction A magnetic force F B is exerted on a charged particle as it moves through a magnetic field B. Since a current is just charged particles in motion, a current carrying a wire also experiences a force when placed in a magnetic field. The magnetic force on a current carrying wire can be given by: (1) 𝐹 𝐵 = 𝐼𝐿 × 𝐵 Where L is a vector that points in the direction of the current with a magnitude equal to the length of the wire. The magnitude of the force is given as: (2) 𝐹 = 𝐼𝐿𝐵𝑠𝑖𝑛(θ) where is the angle between I and B as shown in Figure 2 below. θ If the magnitude is assumed to be perpendicular to the direction of current flow, Equation 2 is simpler than Equation 1. In a current carrying wire, the current is 0 when the wire remains vertical. Once a current is added, it shifts to the side, if current is facing upwards it deflects to the left and if current is facing downwards, the wire deflects to the right. These can be seen in the figure below.
2 Experimental Methods In this experiment, we had 2 parts: For part 1 , we had a wire suspended vertically and passing through a horizontal platform. The wire was also connected to a power supply with a current of 5.0 Amps passing through. A compass was placed on the platform stand near the wire and a map was drawn of the magnetic field produced by the current carrying wire using the compass. For part 2 , we investigated the magnetic force acting on a current carrying wire by observing the change in the weight of the horseshoe magnet. For 2a , we measured the field strength of the horseshoe magnet using the Hall probe. We then picked the current loop with the longest 3-4 sections and this length was recorded. The current loop was placed to the ends of the main unit. We then measured the mass of the horseshoe magnet with no power and increased the current from 0 to 5 Amps in 0.5 A increments. The mass was recorded and it should have been increasing. For part 2b , we used all of the current loops and recorded the change in mass for each as we increased the power from 0A to 5A. This was also recorded. 3 Results and Discussion Part 1 Question: Are your observations of the magnetic field produced by the current consistent with the right-hand rule? Yes, they are. For the top magnetic field, the current is going out making the magnetic field go counterclockwise. For the second part, the magnetic field is going in making the magnetic field go clockwise.
Part 2a Questions: 1. Subtract the mass of the magnet assembly from the mass value in your data table. This is the net mass. Record these values as a column in your data table. Multiply the net mass by g = 9.8 m/s 2 . Why does this value equal the magnetic force FB? Power, I (A) Recorded Mass (g) Net Mass (kg) Magnetic force FB (kg m/s 2 =N) · 0 161.41 0 0 0.50 161.64 0.00023 0.002254 1.00 161.93 0.00052 0.005096 1.49 162.19 0.00078 0.007644 2.00 162.46 0.00105 0.01029 2.50 162.74 0.00133 0.013034 3.00 163.01 0.00160 0.01568 3.50 163.29 0.00188 0.018424 4.00 163.56 0.00215 0.02107 4.50 163.83 0.00242 0.023716 5.00 164.10 0.00259 0.025382 When we use the right-hand-rule, we can figure out that the magnetic force will point in the same direction as the normal force when the current is going right and the magnetic field is pointing towards the surface. The gravitational force also increased when the current was flowing because the normal force increased. So, the net mass multiplied by gravitational force is equal to the magnetic force created by the current carrying wire.
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2. Plot a graph of the magnetic force F versus the current I, and find the slope of the best-fit line from your graph. Slope = 0.00523 kg*m/s^2 / A 3. From Equation 2, the slope of the best-fit line should correspond to LB (product of the length of the 3-4 segment and the magnetic field strength - prove this in the theory section of your report). Using the slope of your graph, find the magnetic field strength of the magnet. Verify this by using the Hall probe and find the percentage difference. The slope of our best fit line is 0.00523. The calculated magnetic field strength is: . Our experimental magnetic field strength was 0.0139 T. The 0. 00523 ÷ 0. 42 = 0. 0126 percent error is . A possible source of error is that this method of 0.0139−0.0126 0.0126 × 100 = 10. 3% measuring the magnetic field strength of the horseshoe magnet is not the most accurate. Part 2b questions: 1. Repeat an analysis similar to steps 1 and 2 from Part 2A for each current loop segment. Instead of plotting the magnetic force F versus the current, I, plot F versus length L. Find the slope of the best-fit line from your graph.
Current Loop Length (m) Mass at I = 0 A (g) Mass at I = 5A (g) Net mass (kg) Magnetic force FB (kg m/s 2 =N) · 0.084 161.41 164.10 0.00269 0.026362 0.064 161.38 163.63 0.00225 0.02205 0.012 161.36 161.78 0.00042 0.004116 0.032 161.37 162.53 0.00115 0.01127 0.042 161.37 162.90 0.00153 0.014994 0.022 161.37 162.16 0.00079 0.007742 Slope = 0.314 2. From Equation 2, the slope of the best-fit line should correspond to IB, the product of the current and the magnetic field strength. Prove this in the theory section of your report. Using the slope of your graph, find the magnetic field strength of the magnet. Compare this with the value obtained by using the Hall probe and that obtained from Part 2A. . The slope of the line was 0.314. The % error is 𝐼𝐵 = 5. 00 × 0. 0139 = 0. 0695 . There are multiple sources of error like the surroundings 0.314−0.0695 0.314 × 100 = 77. 87% impacting our results.
3. Segments 2-3 and 4-5 of the current loop (see Fig 3.) are also within the magnetic field of the assembly. Why are we justified in ignoring the force acting on these segments? Using the right hand rule and assuming the length of segments 2-3 and 4-5 are the same, the direction of the magnitude created by each current will be equal in magnitude but in opposite directions making them cancel each other out. So we can just ignore those forces. 4 Conclusion In conclusion, it is possible to conduct a lab to see the right-hand rule in action and to study the force exerted on a length of a current-carrying wire with changes in current and wire length. For Part 1 of the lab, the right hand rule was apparent in our results. For part 2a of the lab, I had a 10.3% error meaning our data correlated pretty well with the calculations done. For part 2b, I had a 77.87% error which is a really big jump from part A. I don’t entirely understand why such a big percent error occurred, but there could be many multiple sources of error. It could be the accuracy of the scale, the strength of the magnet, the current slowly decreasing as the lab kept going on, and the probe reading might not have been the most accurate. The R 2 was 0.991 for Part 2b so the length of the current and the measured net mass correlated well. The R 2 was 0.999 for Part 1 so the current and the magnetic force calculated correlated even better.
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