lab 6

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Physics

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Dec 6, 2023

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Lorentz Force – Lab Report GOAL: The aim is to explore how particles with electric charge move under the influence of a force called the Lorentz force. Scientists want to understand why these particles move in specific directions. This knowledge helps us learn more about the basics of matter and energy. It also leads to new discoveries in science and technology, shaping our future in exciting ways. PROCEDURE 1: Magnetic Field Intensity and Direction Prediction with charged particle motion to the right , particle’s charge is positive Magnetic field directed out of the screen Direction of force: downward Magnetic field directed into the screen Direction of force: upward Zero Magnetic field Direction of force: zero Table 1: Magnetic Field Strength (T) Radius (m) Force, F B (N) 4 2.25 1.5x10^-8 3 3 1.125x10^-8 2 4.5 7.5x10^-8 1 9 3.75x10^-9 0 ∞ 0 -1 9 -3.75x10^-9 -2 4.5 -7.5x10^-9 -3 3 -1.125x10^-8 -4 2.25 -1.5x10^-8

3. Plot and attach a graph of the Magnetic Field Strength vs. F B : Analysis (Part I) Explain your results. · Observe the paths for the particles that traveled through positive and negative magnetic fields and indicate the direction of the deflection as the particle entered the magnetic field. Upon entering the magnetic field, the particles followed a downward circular trajectory. · Did your prediction match the observed deflected direction? Explain. Once the particle entered the magnetic field sheet, it was inevitable for it to go down in a circular path. · Observe the graphed data. What is the relationship between the force exerted on the moving particle and the intensity of the magnetic field? The force is proportional to the magnetic field.

Observe the path for the particle as it travels through the magnetic field at a strength of +4 T. You will see that even though the initial force is in the downward direction, the particle does not continue downward, but continues to be deflected in a circular arc. Explain why this occurs. This happens because the force is perpendicular to the velocity. PROCEDURE 2: Charge Magnitude and Sign In this procedure you will be observing the relationship of the motion of the charged particle in a magnetic field to its charge. To begin, you will use the default values of the simulation: Mass: 6 ( x10 -25 kg) Velocity: 7.5 (x10 6 m/s) Charge: +5 (x10 -16 C) Magnetic Field Strength: +3 T 4. Use the right-hand rule to predict the direction the charged particles will be deflected when entering the magnetic field: Prediction with charged particle motion to the right , Magnetic field directed out of the screen Neutral Particle (zero charge) Direction of force: No Deflection Positively charged particle Direction of force: downward force Negatively charged particle Direction of force:upward force 5. Run the simulation with the charge values listed in Table 2 and observe the changes in the motion of the particle. Record the radius value (displayed in mm units) and calculate the magnitude of the force on the charged particle as it enters the magnetic field Table 2:

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Charge (C) Radius (m) Force, F B (N) 3 5 mm 67.5x10^6 2 7.5 mm 45x10^6 1 15 mm 22.5x10^6 0 ∞ 0 -1 15 mm -22.5x10^6 -2 7.5 mm -45x10^6 -3 5 mm -67.5x10^6 Analysis (Part II) Explain your results. Observe the paths for the particles that traveled through the magnetic field with various charge values. Indicate the direction of the deflection of the particle for positive , negative , and zero charge. When the value was a positive charge the direction of the particle was downwards. When the charge was negative the particles went in the upward direction, and when the charge was zero it stayed neutral. Did your prediction match the observed deflected direction? Explain. My predictions did match the observed directions because it contrasted the charge of the particles. PROCEDURE 3: Charged Particle Velocity In this procedure you will observe the affect of velocity on the charged particle’s motion in a magnetic field. 1. Navigate to the following simulation: https://ophysics.com/em8.html The simulation has the following controls available: · m: mass · q: charge · v o x: Initial Velocity (x-direction, perpendicular to magnetic field)

· v o z: Initial Velocity (z-direction, parallel to magnetic field) · b: magnetic field intensity 2. The simulation will show the path of a charged particle moving in a uniform magnetic field. Before you run the simulation, use your knowledge of the concepts we have built so far to predict the effect that changes to the particle’s velocity will have on its trajectory in the magnetic field. You can state your prediction in terms of the radius of the circular path, or any change to the path. Explain your reasoning for your predictions Prediction with fixed uniform magnetic field, motion starts as a circle with radius r 0 . Increasing initial velocity, v o x (perpendicular to field) Change in particle’s motion: bigger area Explanation: since the field is perpendicular , the velocity will increase perpendicular. Increasing initial velocity, v o z (parallel to field) Change in particle’s motion: The particle will go in circular rotations. Explanation: The radius will remain the same. 3. Run the simulation with the following values and attach screenshots of the motion using both “View from Above” and “View in 3D” · v o x = 5, v o z = 0 · v o x = 2, v o z = 0

· v o x = 7, v o z = 0 · v o x = 5, v o z = 0.2 · v o x = 5, v o z = 0.4

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Analysis (Part III) Explain your results. After your observation of the particle, what is the overall effect of increasing velocity perpendicular to the field on the trajectory of the particle? The field will increase in its size. In the previous procedures, we observe that as the Lorentz force increases, the radius of the circle becomes smaller. The formula F = qvB suggests that the force should be increasing linearly with velocity, however the radius is increasing instead of decreasing. Explain why this occurs. Hint: you may need to refer to the centripetal force formula. When moving in circular paths, the magnetic force will be equal to the centripetal force, therefore the equation of the force will be the following : F=mv^2/r. In this case m is the mass, v the velocity and r is the radius of the circular path. Therefore: Fc=Fm Mv^2/r=qv x B R=mv/qB Thanks to this we can see that the radius of the circle increases with the increase of velocity. What is the overall effect of increasing velocity parallel to the field on the trajectory of the particle? The overall effect that it will have on the trajectory is that it will be higher. Use the Lorentz Force formula to explain how increasing the velocity parallel to the magnetic field does not affect the force exerted on a particle within the magnetic field.

If the charged particle velocity is parallel to the magnetic field, then there will be no net force and the particle will be moving in a straight line.

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