PHY100 Homework 4 (1)

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PHY100 Homework 4 Weight 8% 1. Special Relativity: Consider a firecracker that after being triggered explodes after 1 second. An observer A is standing some distance away from observer B who is traveling with constant velocity towards A with the firecracker. The velocity of B and distance between A and B is such that B will reach A in 1 sec as measured by A. At this instant B triggers the firecracker they are holding. Which of following options is correct. a. The firecracker explodes exactly when B reaches A b. The firecracker explodes before reaching A c. The firecracker explodes after crossing A d. All the above outcomes are possible Explain your answer. (20 pts) The correct option is d. It is essential to note that the manner in which an event occurs can change depending on various factors which are stated in the principles of special relativity. One main concept to consider is time dilation. This is when the relative motion of two observers in different reference frames causes them to perceive time differently. Since observer B is moving and observer A is still, time is moving more slowly for observer B, which can change the way things are seen from their perspective. This is linked to idea of simultaneity; an event that appears one way to one observer may not appear the same way to another observer. For these reasons, all of these options are possible depending on which frame of reference we are considering. 2. Educating ancients: a. How does a glass rod after being rubbed on silk exerts force on another charged object? (7 pts) Glass is a material that can lose electrons easily. So, when it is rubbed on silk it will become positively charged. The silk on the other hand, will gain electrons and become negatively charged. Because of this charge difference, the glass rod should exert a force on other objects. If the object is positively charged, the rod will repel it. If the object is negatively or neutrally charged, the rod will attract it. b. Describe an experiment that you could use to show that there are two kinds of charges? (13 pts) The balloon and sweater experiment can illustrate the different kinds of charges. In this experiment, a balloon and a sweater each start out with a neutral charge (same amount of protons as electrons). However, when the balloon is rubbed against the sweater, the balloon gains the sweaters' protons. As a result, the balloon will be positively charged and the sweater will be negatively charged. Since opposite charges tend to attract, the balloon will stick to the sweater. Similarly, if we bring the balloon close to a neutrally charged wall, we will also see some attraction. On the contrary, if we take a second positively charged balloon, the two balloons will repel due to their identical charges. 3. Fields (electric and magnetic) around a charged object: a. What field(s) does a stationary (non-magnetic) charged object produce? (7 pts) A stationary charged object produces an electric field. It is only when the object starts moving that a magnetic field occurs.

b. Does a moving charge particle produce both electric and magnetic field? Explain your answer. (13 pts) Yes, a moving charged particle does produce both an electric and magnetic field. As mentioned in the previous question, when a particle is stationary, it has only an electric field. A changing electric field occurs when the particle starts to move; this produces a magnetic field. This particle oscillation is considered to be an electromagnetic wave, which is also light. 4. Electromagnetism: Consider two balls (starting at zero speed) rolling down under the force of gravity (the direction of force by gravity is shown by the arrow) inside conducting copper (nonmagnetic material) tubes; the red ball is magnet and blue is not. (This is exactly the situation we discussed in class with a demonstration.) a. Are current produced in either tube? Explain your answer. (10 pts) There is a current produced in the red ball’s tube but not the blue one. Since the red ball is magnetic, it will create a changing magnetic field inside the tube as it travels. This changing magnetic field will result in an electric field, which creates a current. Since the blue ball doesn’t possess any magnetism, this will not occur. b. What is the direction of electromagnetic force on the two balls, if any? Which ball will reach the end of the tube first? (15 pts) Since the blue ball is not magnetic, it will not experience an electromagnetic force. Because of this, there is only the downward force of gravity that is acting on it. There will however be an electromagnetic force exerted on the red ball in the upward direction. This force is in the opposite direction as gravity and is therefore resisting the ball’s downward motion. As a result, the blue ball will reach the end of the tube first. c. Can the red ball reach the end (bottom) of the tube first? Explain. Hint: Conservation of energy. (15 pts) No, the red ball cannot reach the bottom of the tube first due to the conservation of energy. According the this law, the total energy in the system should remain constant, assuming there are no external forces acting on it. So, if we somehow got the the red ball to lose some of its magnetism (via heat perhaps), its kinetic energy and potential

energy should still stay the same regardless. Magnetism is not correlated to energy. Thus, there is no way for the red ball to reach the bottom faster than the blue ball. d. Can the system be rigged in a way that the magnetic ball is stable with zero velocity and no net forces (without changing the configuration of the set up and the material of the tubes)? Explain your answer. (Bonus 15 pts) The only way this could be accomplished would be to increase the ball’s magnetism so that it offsets the force of gravity enough. The best way to do this would be to freeze the ball to a very low temperature. This way, the protons in the ball will not move around very much. Consequently, it will be easy for the electrons to move around and create a stronger current, thus having a stronger magnetic force. If this magnetic force exceeds a certain point, it is possible that the ball will not be able to move down the pipe at all. In this case, this strong force combined with the opposing force of gravity will add up to create a zero net force.

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