Lab 8 - Magnetism (1)

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Name ___________________________ Date___________________ MAGNETISM SIMULATION Introduction In this simulation you explore magnetic fields and their effect, through the Lorentz force law, on charged particles. 1 – The Magnet Open the simulation (https://www.geogebra.org/m/g9DXB8AD) A rectangular magnet is displayed 1. Which pole does the red end of the magnet represent? The red end represents the north pole. 2. What do the black lines with an arrow drawn on them represent? The black lines with an arrow drawn on the magnet represent the magnetic field lines. 3. Do any of the lines in question 2 leave the magnet and go to infinity? Magnetic field lines are continuous to forming closed loops without beginning or end. They go from the north pole to the south pole. Therefore, no there are no line that go to infinity. 4. In which location is the magnetic field strongest? At the poles the magnetic field is strongest.
2 – The Lorentz Force in 3D Open the simulation (https://www.geogebra.org/m/xpRMzPgc). The simulation displays the motion of charged particles in a magnetic field.
The applet displays the motion of both in a magnetic field (red lines). In the upper part of the screen the motion is shown in 2D and in the lower part of the screen the full 3D motion of a charged particle in the magnetic field is shown. Set the y and the z components the velocity to zero. 5. Which of the two particles is positive? The P particles is positive. 6. Which of the two particles is negative? The Q particle is negative. Press play and watch the motion in 2D. 7. What direction does the positive particle rotate ? The positive particles move clockwise. 8. What direction does the negative particle rotate? The negative particles move counterclockwise. Set the z components the velocity to 1m/s 9. What shape do the particles trace out as they move in 3D? A circle. The circles that the particles trace out in the plane have a radius given by r = mv qB and the period of motion is given by T = 2 π qB m If you increase the mass of the particle, 10. How does the radius of the circle change? As r ∝ m, if mass decreases then the radius of the circle decreases. 11. How does the period of the motion change? As T ∝ m, if mass decreases then the time period decreases. If you increase the magnetic field, 12. How does the radius of the circle change? As r ∝ 1/B, if B decreases then the radius of the circle increases. 13. How does the period of the motion change? As T ∝ 1/T, if B decreases then the time period increases. If you decrease the charge of the particle,
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14. How does the radius of the circle change? As q ∝ 1/r, if the charge increases then the radius decreases. 15. How does the period of the motion change? As q ∝ 1/T, if the charge increases then the time period decreases. If you increase the x components of the velocity 16. How does the radius of the circle change? As Vx ∝ r, decrease in the component of velocity decreases the magnitude of radius. 17. How does the period of the motion change? As Vx ∝ 1/T, decrease in x component of velocity increases the period. 3 – Magnitude of the Lorentz Force The magnitude of the Lorentz force is given as, F = q v B sin( θ) Suppose that a physicist sets up a region of uniform magnetic field. A sphere of an unknown charge is going to be shoot into the region perpendicular to the direction of the uniform magnetic field with a velocity of v = 100 m/s. The physicist then measures the force on the charged sphere. The following table contains the data of the measurements F (μN) 50.17 101.82 150.71 209.33 266.05 319.65 361.59 432.18 493.34 543.76 B (T) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Plot F vs B. 18. What is the slope of the line? (Cm/s) Slope = change in F / change in B = ((493.34-50.17) x 10^-3) / (0.9 – 0.1) = 5.52 x 10^-4 C m/s 19. What is unknown charge on the sphere? (μC) q = (5.52x 10^4)/100 = 5.52 μC As we saw above when charged particles move through regions of magnetic fields they make circles in the plane. Consider the charged sphere used by the physicist in the previous problem when B=0.5T (the velocity is still v = 100 m/s), if the mass of the sphere is m =5 x 10 -8 kg:
20. What is the radius of the circle traced out by the charged sphere? (m) r = (5 x 10^-8 x 100)/(5.52 x 10^-6 x 0.5) = 181.156 x 10^-2 m 21. What is the period of the motion? (s) T = (2 𝜋 x 5 x 10^-8 ) / (5.52 x 10^-6 x 0.5) = 0.113826 s 22. What is the angular frequency ω = 2π/T ? (rad/s) w = 2 𝜋 / 0.113826 = 55.2 rad/s 4 – Map the Field Lines Open the simulation (https://www.compadre.org/Physlets/electromagnetism/ex27_1.cfm)
Underneath the gray circle is a source for a magnetic field. Use the compass to explore the directions of the magnetic field around the object. If you click and hold the simulation will show coordinates in the bottom left of the window. Select Configuration 1. In which direction is the compass pointing... 23. In the region on the left of the source? The compass needle points towards the source, indicating the magnetic field lines are entering the source from this side. 24. In the region beneath the source? The compass needle points away from the observer and towards the source, suggesting the magnetic field lines are directed upwards towards the source in this region. 25. In the region on the right of the source? The compass needle points away from the source, indicating the magnetic field lines are exiting the source from this side. 26. In the region above the source? The compass needle points towards the observer and away from the source, suggesting the magnetic field lines are directed downwards away from the source in this region. 27. What is the source of the magnetic field? A bar magnet, with the magnetic field lines exiting from one end (which can be considered the magnetic north pole) and entering the other end (the magnetic south pole). The compass directions (pointing towards the source on the left, away on the right, upwards beneath, and downwards above) are consistent with the magnetic field pattern created by such a magnet. Select Configuration 2. In which direction is the compass pointing... 28. In the region beneath the source (x= 0, y=-1)? The compass points in the direction of the magnetic field line at that point. If we assume a standard magnetic field setup like that of a bar magnet or similar, the compass beneath the source would typically point upwards towards the source, indicating the magnetic field lines are directed from south to north outside the magnet. 29. In the region to the right of the source (x= 1, y=0)? Here, the compass would align itself tangentially to the magnetic field lines. In a conventional setup, this would mean the compass points towards the top of the screen/page if we assume the north pole of the source is directed upwards. 30. In the region to the left of the source (x= -1, y=0)? Similarly, the compass aligns tangentially to the magnetic field lines, pointing towards the bottom of the screen/page if the north pole of the source is upwards, indicating the magnetic field lines curve around the source. 31. In the region above the source (x= 0, y=1)? The compass here would typically point downwards away from the source, following the direction of magnetic field lines that emerge from the north pole and loop back towards the south pole. If you double click on any point the simulation displays the magnetic field lines. Draw as many lines as needed in order to answer the following question. 32. What is the source of the magnetic field? Circular loop.
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5 – Two Wires Carrying Currents Open the simulation ( http://physics.bu.edu/~duffy/HTML5/BField.html) Set the current on the left to -5 A, current on the right to zero. 33. In which direction is the current? The current is going clockwise. Set the current on the left to +5 A, current on the right to zero 34. In which direction is the current? The current is moving counterclockwise. Set the both current to the same value 35. Is there a point where the magnetic field is zero? The magnetic fields is zero right in between the fields of the two points. 36. In which direction is the magnetic field pointing in the center? The top arrow is pointing to the left and the bottom arrow is pointing to the right. Right in the center there is just a dot. Set the current on the left to 10 A, current on the right to -10 A 37. In which direction is the magnetic field pointing in the center? It is pointing upwards.

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