Electric field strength

Question: (i) State what is meant by a field of force. (H2 2012 P3 Q7)

Possible Answer: A field of force is a region in space where a particle experiences a force.

Further details: Strictly speaking, a field is not just a region in space. There is also no agreement on how the field of force should be defined. For example, one may consider the field to be a medium in space instead of simply space. Furthermore, a textbook author may state that a field of force exists in a region in space where a particle experiences a force (Hecht, 2003). However, one may analyse the definition of a field from the following perspectives: (1) a region in space (condition); (2) a particle (object); (3) experiences a force (effect).

 

Question: (ii) Define electric field strength

Possible answer: Electric field strength is the electric force per unit charge acting on a test charge that is stationary.

Further details: An alternative definition of the electric field strength is the electric force per unit charge experienced by an infinitely small test charge placed in a vacuum having an electric field. Mathematically, it is given by the equation E = F/q, where F is the electric force experienced and q is the infinitely small test charge. This is because a large test charge will influence the charge carriers in the surrounding and distort the electric fields. (Note that physics educators may prefer the term charge carrier as compared to charge because charge is an attribute of an object.)

 

Question: (iii) Suggest why, when defining electric field strength, the test particle must be stationary.

Possible answer: In a region in space, it is possible to have gravitational fields, electric fields, and magnetic fields. Thus, we should specify the condition that the test particle is stationary because the measured force could include magnetic force for the moving test particle in addition to the electric force.

Further details: Some physics teachers explain that a moving charge produces electromagnetic waves which are perpendicular electric and magnetic fields, and hence it will distort the original field in the region. Physics students should question these teachers on the source of wave energy. Strictly speaking, it is the accelerating charge carrier that produces electromagnetic waves.

Reference:

Hecht, E. (2003). Physics: Algebra/Trigonometry (3rd ed.). Pacific Grove, California: Brooks/Cole Publishing.

Diffraction and polarisation

Question: Explain, using diagrams, what is meant by the terms diffraction and polarisation of waves.

Diffraction: Diffraction refers to a phenomenon by which there is a spreading of waves through an opening or a bending of waves around an obstacle (see figure 1 below). Diffraction of waves can be observed if the size of the opening or obstacle is comparable to the wavelength of the waves.

diffraction
Figure 1

Further details on diffraction: According to Einstein and Infeld (1966), “the diffraction of light, the deviation from the rectilinear propagation when small holes or obstacles are placed in the way of the light waves (p. 115).” Historically speaking, Italian philosopher Francesco Grimaldi coined the term diffraction and showed how a single beam of light spreads out through very small slits. However, a mark scheme states that “with the presence of an obstacle, light spreads round it into region that would be in shadow if the light travelled in straight lines. Behind the obstacles or apertures at which diffraction occurs, a diffraction pattern of dark and bright fringes can be observed.” Importantly, diffraction of light is likely observable if the size of an opening or obstacle is comparable to the wavelength of light (from 4 × 10-7 m to 7 × 10-7 m.)

Polarisation: Polarisation refers to a phenomenon by which the oscillation of waves is confined to a single plane after passing through a polariser (see figure 2 below). The waves are transverse in nature such that the plane of oscillations contains the displacement of waves and the direction of energy transfer.

polarised
Figure 2

Further details on polarisation: Strictly speaking, there is no unpolarised light. In the words of Feynman, “We have considered linearly, circularly, and elliptically polarized light, which covers everything except for the case of unpolarised light. Now how can the light be unpolarised when we know that it must vibrate in one or another of these ellipses? If the light is not absolutely monochromatic, or if the x– and y-phases are not kept perfectly together, so that the electric vector first vibrates in one direction, then in another, the polarization is constantly changing. Remember that one atom emits during 10−8 sec, and if one atom emits a certain polarization, and then another atom emits light with a different polarization, the polarizations will change every 10−8 sec. If the polarization changes more rapidly than we can detect it, then we call the light, unpolarised, because all the effects of the polarization average out. None of the interference effects of polarization would show up with unpolarised light. But as we see from the definition, light is unpolarised only if we are unable to find out whether the light is polarized or not. Feynman et al., section 33–1 The electric vector of light)”.

A mark scheme on the meaning of polarisation is “the (wave) oscillations occur only in one plane”. In addition, another mark scheme states that “polarised light: (The electric field vector of) the wave oscillates or vibrates in one plane”. However, an important condition for polarisation is that the waves should be transverse in nature such as light waves.

Below is a table comparing the phenomena diffraction and polarisation.

  Diffraction Polarisation
cause An opening or obstacle A polariser
characteristic Spreading or bending of waves Oscillating or vibrating of waves in one plane
condition The size of opening or obstacle is comparable to the wavelength of waves The oscillation of waves is perpendicular to its direction of motion or energy transfer

References:

  1. Einstein, A., & Infeld, L. (1966/1938). The Evolution of Physics. New York: Simon and Schuster.
  2. Feynman, R. P., Leighton, R. B., & Sands, M. (1963). The Feynman Lectures on Physics, Vol I: Mainly mechanics, radiation, and heat. Reading, MA: Addison-Wesley.

Bungee jumping I

Question: The momentum of the person increases during free fall. Explain whether or not this is a violation of the principle of conservation of momentum. (H1 2008)

Answer: The momentum of the person increases during free fall because of an “external” gravitational force. The principle of conservation of linear momentum holds if there is no external force acting on the person. However, there is an external gravitational force acting on the person in this case.

Further details: Alternatively, we can consider the person and the earth to be a system. In this case, the increase in the downward momentum of the person equals to the upward momentum of the earth. However, the mass of the person is relatively very small as compared to the mass of the earth. Thus, the upward velocity of the earth is negligible. More importantly, we can consider the gravitational force to be an internal force for the person-earth system.

Question: Explain why it would be extremely dangerous to have a bungee rope that is much stiffer. (H1 2008)

Answer: If the rope is more elastic, the person would be stopped in a longer period of time. This implies a lower resistive force and a longer extension of the rope for the person to decelerate. On the contrary, a much stiffer bungee rope will cause a much higher resistive force and a very shorter extension of the rope to stop the person. The larger force can result in serious injury, and thus, it is extremely dangerous.

Further details: By using v2 = u2 + 2ax, we can rewrite the equation as a = (v2u2)/2x. If the rope is much stiffer, it means the extension will be very short. Thus, the magnitude of acceleration will be very large based on the equation. By using Newton’s second law of motion, F = ma, higher acceleration means greater force. However, the elasticity of bungee rope can also cause more energy to be stored in the rope. As a result, the person will oscillate for a while before the motion is finally stopped.

Note:

1. For a fatal accident relating to bungee jumping, please refer to this website:

http://www.telegraph.co.uk/news/worldnews/europe/spain/11754881/British-woman-23-dies-in-bungee-jump-accident-in-Spain.html

2. For a demonstration of bungee jumping, you can visit the following youtube video:

Importance of frictional forces

Question: Friction is often regarded as a nuisance. State two different situations where friction is of critical importance.

  1. While a car is moving at high speed, there must be sufficient frictional force between tyres and a road surface such that we can increase or decrease the speed of the car. If there is no kinetic frictional force between the tyres and the road surface, we cannot even accelerate or decelerate the car.
  2. The floors in a building should have sufficient frictional force such that we do not slip and fall. There are fatal accidents such as elderly slips and falls in a bathroom. (Similarly, when we place objects such as glass bottles on a table, it is the static frictional force that keeps the glass bottles at rest. If there is no static frictional force, a gentle breeze can cause the glass bottles or any objects to slide and fall onto the ground.)

 

Question: For one of your examples explain why friction is so important.

The need of sufficient frictional force between the car’s tyres and road surface is extremely important for road safety. When the coefficient of friction between the tyres and the road surface is relatively low, we will have difficulties to decelerate and stop the car within a short period of time, and this can result in traffic accidents. That is why traffic accidents happen more frequently because of rains or snows.

 

Further details: There is a close correlation between the frictional force of road surface and risks of traffic accidents. For instance, worn tyres are likely to contribute towards traffic accidents in wet conditions of roads as compared to dry conditions. For a discussion of frictional force of bathroom, you can visit the following website:

 

Note:

Feynman has a good explanation of frictional force: “We have just discussed two cases of friction, resulting from fast movement in air and slow movement in honey. There is another kind of friction, called dry friction or sliding friction, which occurs when one solid body slides on another. In this case, a force is needed to maintain motion. This is called a frictional force, and its origin, also, is a very complicated matter. Both surfaces of contact are irregular, on an atomic level. There are many points of contact where the atoms seem to cling together, and then, as the sliding body is pulled along, the atoms snap apart and vibration ensues; something like that has to happen. Formerly the mechanism of this friction was thought to be very simple, that the surfaces were merely full of irregularities and the friction originated in lifting the slider over the bumps; but this cannot be, for there is no loss of energy in that process, whereas power is in fact consumed. The mechanism of power loss is that as the slider snaps over the bumps, the bumps deform and then generate waves and atomic motions and, after a while, heat, in the two bodies. Now it is very remarkable that again, empirically, this friction can be described approximately by a simple law. This law is that the force needed to overcome friction and to drag one object over another depends upon the normal force (i.e., perpendicular to the surface) between the two surfaces that are in contact. Actually, to a fairly good approximation, the frictional force is proportional to this normal force, and has a more or less constant coefficient; that is, F = μN, where μ is called the coefficient of friction (Feynman et al., 1963, section 12-2 Friction).”

Reference:

Feynman, R. P., Leighton, R. B., & Sands, M. (1963). The Feynman Lectures on Physics, Vol I: Mainly mechanics, radiation, and heat. Reading, MA: Addison-Wesley.

Photoelectric emission

Question: (a) Explain the phenomenon of photoelectric emission by referring to photon energy and work function energy. (H1 2013)

Photoelectric emission refers to the phenomenon in which light waves of sufficiently high frequency (or short wavelength) eject photoelectrons from the surface of various metals. Based on the law of conservation of energy, the photon energy (hf) of light waves equals to the work function energy (Փ) of the metal and the maximum kinetic energy (K.E.max) of a photoelectron (i.e. hf = Փ + K.E.max). Essentially, a light wave can behave like a particle (or a photon) when it interacts with an electron in the metal’s surface.

Further details:

In a seminal paper titled On a Heuristic Point of View Concerning the Production and Transformation of Light, Einstein (1905) writes that “it seems to me that the observations of ‘blackbody radiation,’ photoluminescence, production of cathode rays by ultraviolet light, and other related phenomena associated with the emission or transformation of light appear more readily understood if one assumes that the energy of light is discontinuously distributed in space. According to the assumption considered here, in the propagation of a light ray emitted from a point source, the energy is not distributed continuously over ever-increasing volumes of space, but consists of a finite number of energy quanta localized at points of space that move without dividing, and can be absorbed or generated only as complete units (p. 178).” In other words, Einstein (1905) proposes that the incident light rays consist of individual energy quanta, called photons, that interact with the photoelectrons in the surface of the metal like discrete particles, instead of continuous waves.

Question: (b) Explain why the maximum energy of photoelectrons is independent of intensity whereas the photoelectric current is proportional to intensity. (H1 2013)

Based on the experimental results, if the light intensity is doubled, the number of photoelectrons ejected is doubled, but the maximum energy of photoelectrons remains unchanged. In other words, an increase in the intensity of light means an increase in the number of photons per unit time and thus, it results in an increase in the photoelectric current or number of photoelectrons emitted. Essentially, the energy of a photon is quantized and a photon interacts only with a photoelectron from the surface of the metal.

Further details:

Using the classical Maxwell’s theory of light, the more intense the incident light rays, the greater the kinetic energy of photoelectrons should be ejected from the metal. However, what the question has asked is about single-photon photoelectric effect. Strictly speaking, it is not true that an increase of light intensity cannot increase the maximum kinetic energy of photoelectrons emitted. For example, a laser (or more intense light rays) can produce the multiple-photon photoelectric effect in which the maximum kinetic energy of photoelectrons can be increased (Georges, 1995).

 

References:

Einstein, A. (1905). On a Heuristic Point of View Concerning the Production and Transformation of Light. In J. Stachel (ed.) Einstein’s Miraculous year: Five papers that changed the face of physics. Princeton: Princeton University Press.

Georges, A. T. (1995). Theory of the multiphoton photoelectric effect: A stepwise excitation process. Physical Review B, 51(19), 13735.

Adjustments of musical instruments

Question: Explain why musical instruments that produce low frequency notes are larger than those that produce higher frequency notes. (H1 2014)

Answer:

When the length of air column (or string) of a musical instrument is half of a wavelength of sound waves, it can result in the formation of stationary waves. Thus, the amplitude of the sound waves produced by the musical instrument is significantly larger at its natural (or resonant) frequency. In other words, as the speed of the sound waves is relatively constant, the frequency (f = v/λ) of the sounds or notes is inversely proportional to the wavelength of the sound waves or the length of the air column.

Further details:

In general, the musical instruments produce a range of frequencies instead of only a natural frequency or a resonant frequency. However, the resonance phenomenon occurs in which the amplitude of forced oscillations of the sound waves reaches a maximum when the driving frequency of a source (e.g. the mouth of a musician) equals to the natural frequency of the musical instrument.

 

Question: The speed of sound in air increases as the temperature rises. During a concert, the temperature in a concert hall increases and musicians playing instruments such as trumpets and flutes need to adjust the lengths of their instruments to keep the instruments in tune. State and explain what adjustment needs to be made. (H1 2014)

Answer:

A short answer could be simply: ‘the length of the musical instruments should be adjusted slightly longer such that the sound waves remain in the same frequency. This is because the wavelength of the sound waves is slightly longer as the temperature rises’. However, to be more precise, we can explain that the flute should be lengthened by using a tuning slide such that the pitch or frequency of the sound waves remains unchanged. As the velocity and the wavelength of the sound wave increase with the temperature, the distance between the mouthpiece and the other end of the musical instruments should be increased such that it can result in the formation of stationary waves or resonance phenomenon.

Further details:

The temperature can affect the sound waves of musical instruments in several ways, which can be different depending on the musical instrument. Thus, musical performances are dependent on indoor or outdoor in which the surrounding temperature also tends to expand the musical instruments, and thus, change the tension of the string instruments, which may change their interactions with musicians. However, some musicians believe that cooling a musical instrument to extreme temperatures can improve its tone. Both trumpet and flute players have been known to freeze their instruments in the fridge for some days, and describe the sound that comes out of the cooler instrument as ‘more mellow’. On the contrary, there are also reports that there is no significant difference by cooling the musical instruments.

 

In general, you can change the effective lengths (or air column) of a flute by opening and closing holes of the flute with your fingers. On the other hand, you can change the effective lengths of a trumpet by routing the mouthpiece to the bell through different folded up tubes with the valves on the trumpet.

 

References:

  1. Olson, H. F. (1967). Music, Physics and Engineering. New York: Dover.
  2. Does temperature affect the sound of a musical instrument?

http://www.scientificamerican.com/article/does-temperature-affect-instrument-sound/

Geostationary orbit

Question: Explain what is meant by the term geostationary orbit.

Answer: A geostationary orbit is a circular orbit around the Earth in which a satellite would appear stationary relative to an observer on the Earth.

Further details:

  • “Time”: The period of revolution of a geostationary satellite must be 24 hours.
  • “Location”: A geostationary satellite must be directly above the equator.
  • There is only one possible radius for a geostationary orbit: 42.3 X 107m from the centre of the Earth. (The distance can be calculated by using the equation, a = GM/r2 = ω2r.)

Reference:

The electron’s path for the minimum speed

Question: An electron, initially at rest a long distance from the spheres in (b), approaches the spheres and passes between the two spheres. Describe the path of the electron for the minimum speed in (i).

Answer: The electron increases its speed and it approaches the two spheres in a straight line. Subsequently, the electron moves in a to-and-fro motion (NOT simple harmonic motion!) within the same straight line because the net force is zero in the x direction. Furthermore, the net force on the electron is not directly proportional to its displacement from the “centre” of motion.

Further explanation: The electron does not move at a constant speed because the electric force due to a charged sphere is inversely proportional to the square of the distance between the centre of the sphere and the electron. However, in the real world, the electron tends to be attracted to the sphere that is at a higher potential. (More importantly, the question should be worded more clearly.)

Ascending Bubbles in a fizzy drink

Question: Suggest why larger bubbles move with a greater velocity towards the surface than do smaller bubbles.

My proposed answer: The upthrust or buoyant force on the bubbles is directly proportional to its volume (Archimedes’ Principle). In addition, the volume of a larger bubble increases significantly because of lower hydrostatic pressure as it ascends. On the other hand, the drag force on the bubbles is proportional to its radius and velocity (Stokes’ law). Thus, the larger bubble moves with a greater velocity towards the surface because the upthrust is significantly greater than the drag force.

Further detail: The drag force, F = Br²ρv², is applicable for turbulence flow or high Reynold’s number. However, the Reynold’s number for an ascending bubble is found to be below 50 in Shafer and Zare’s (1991) experiment. Strictly speaking, the drag force on an ascending bubble is a complicated function of its radius, speed, as well as the viscosity, density and surface tension of the liquid that it is in. If the ascending bubble had a fixed size, it would quickly reach a terminal speed at which the buoyant force equal to the drag force. However, the increase of ascending bubble’s radius causes a further increase in the buoyant force, and thus, it has a greater acceleration as compared to a smaller bubble.

Question: Suggest why the velocity of an ascending bubble remains almost constant when a bubble is very small.

My proposed answer: the upthrust or buoyant force on a very small bubble is significantly lower as compared to a larger bubble. As the very small bubble ascends, its expansion is negligible and the buoyant force on it does not significantly increase. Thus, the net force on the small bubble is close to zero because the drag force could increase due to the increase in velocity, and it may almost equal to the magnitude of the upthrust.

Further detail: Theoretically, physicists may assume the bubbles to double its size if they move up about 10 metres. This is because the hydrostatic pressure due to water of “10 metres height” is about 1 atmospheric pressure. However, ascending bubbles act as nucleation centres and accumulate carbon dioxide as they ascend through a beer or fizzy drink.

Reference:
Shafer, N. E., & Zare, R. N. (1991). Through a beer glass darkly. Physics Today, 44(10), 48-52.

Ideal Transformer

​Question: Use Faraday’s law to explain whether the output and the input potential differences are in phase.

Physics teachers may expect the following answer: “the output and the input potential difference are out of phase. According to Faraday’s law of electromagnetic induction, the induced electromotive force (output potential difference) is directly proportional to the rate of change of magnetic flux linkage of the transformer (Es = -Ns dΦ/dt). Essentially, the electromotive force is induced in the secondary coil to oppose the alternating magnetic fields (or flux) in the primary coil.” The negative sign in the equation Es = -Ns dΦ/dt (Faraday’s law) is sometimes labeled as Lenz’s law.

Interestingly, a similar question can be found in Cambridge International A Level Physics 9702 Syllabus (General Certificate of Education) Year 2009 Paper 42 Question 6 (b) (ii): “Use Lenz’s law to explain why input potential difference and output e.m.f are not in phase.” The marking scheme states that: “(induced) current in secondary produces magnet​ic field (M1); opposes (changing) field produced in primary (M1); so not in phase (A0).” No mark is awarded for stating the input potential difference and output electromotive force are not in phase because this is already specified in the question. Thus, it is incorrect to use the equation Vs = -Ns dΦ/dt​ to explain that the output and the input potential differences are in phase.

Importantly, students can understand the direction of induced current from the perspective of the principle of conservation of energy (Reese, 2000). If we assume there is no energy loss in the transformer, the sum of power absorbed by the primary coil (IpVp) and the secondary coil (IsVs) is always zero.
Therefore, IpVp + IsVs = 0 implies Is = -(Vp/Vs) Ip = -(Np/Ns) Ip
The negative sign could be explained as follows: if primary current (Ip) is flowing into the primary coil, then secondary current (Is) is flowing out of the secondary coil, or vice versa.

Further discussions of this question can be found at the following website:
http://feynman-answer.blogspot.sg/2016_03_01_archive.html

Reference:
Reese, R. L. (2000). University Physics. Pacific Grove, California: Brooks/Cole.