IB Physics Magnetic Field
/When a current flows in a wire a magnetic field is created around the wire. Is there a magnetic field inside the wire?
Dr Stephen McAndrew
What are the concepts in Physics and Mathematics that students find difficult? In this blog I will post tutorial sheets that I hope will stimulate thinking and so broaden the knowledge and understanding of students allowing them to write thorough examination responses. Tutorial sheets, structured to assist student learning, will be posted on IB SL and HL Physics syllabus topics as well as the general HSC topics of relativity, electromagnetism, mechanics, thermodynamics, quantum physics and calculus. The overall purpose of these pages is to encourage and promote learning in Physics and Mathematics and so open new horizons in learning.
When a current flows in a wire a magnetic field is created around the wire. Is there a magnetic field inside the wire?
Two straight parallel wires carrying currents in the same direction attract each other. Two electron beams travelling in the same direction repel each other. Why?
One of the most misunderstood concepts in the quanta to quarks section of the current NSW HSC Physics syllabus is binding energy. Listed below are some tutorial points on this concept.
One of the most difficult and misunderstood concepts in the ideas to implementation section of the current NSW HSC Physics syllabus is band theory. Listed below are some tutorial points on this concept.
One of the most difficult and misunderstood concepts in the space section of the current NSW HSC Physics syllabus is simultaneity. Listed below are some tutorial points on this concept. Two sentences from Einstein's own popular exposition on relativity, Relativity, the Special and General Theory, Methuen, 1920, are given italics.
During the next 4 weeks I will list the most misunderstood concept in each of the four sections of the current NSW HSC Physics syllabus. Back emf is the most misunderstood concept in the motors and generators section. Here are some tutorial points on back emf.
The IB Physics examination papers are on October 31 and November 1. From now until this date I will list questions to help students revise for their Physics examination. This list will be updated over the next six weeks.
Students can increase their marks significantly during this period if they are positive, organised and have a plan. What is required is a balanced approach to study with adequate nutrition, sleep, exercise and recreation.
The HSC Physics examination is on October 30. From now until this date I will list questions to help students revise for their Physics examination. This list will be updated during the next two months.
Students can increase their marks significantly during this period if they are positive, organised and have a plan. Remember that the HSC Physics examination is not "difficult Physics". What is required is a steady approach to study with adequate nutrition, sleep, exercise and recreation.
The HSC Physics topic Quanta to Quarks includes the concept of the wave nature of an electron.
In electromagnetism and fluid dynamics we often determine the curl of a vector quantity. This is a mathematical operation that follows set rules and is used to determine a field vector. What does curl mean physically?
In electromagnetism when rationalised SI units are used, the curl of the electric field vector (E) is equal to minus the partial time derivative of the magnetic induction vector (B) and the curl of the magnetic field vector (H) is equal to the sum of the current density (J) and the partial time derivative of the electric displacement vector (D). These relationships are known as the Faraday-Maxwell law and the Ampere-Maxwell law respectively. In fluid mechanics the curl of the fluid velocity vector (u) is equal to the vorticity (W).
The curl operation is a mathematical way of determining whether the work done (also called the circulation) in moving around a small circle centred at the field point is zero. If the work done is zero the field is said to be conservative or irrotational, meaning that a small paddle wheel placed at that point in the field would not spin if the field was the velocity field of a fluid, hence the name of the operation curl. Some textbooks call the curl operation rot, the significance coming from the rotation of the test paddle wheel. The mathematical rule connecting curl with work done is known as Stokes' theorem, one of the very important theorems of vector analysis along with those of Gauss and Green.
The curl operation is a very important part of the language of electromagnetism. The curl operator is part of the mathematical language that we use to show that time varying electric and magnetic fields propagate through space at the speed of light.
In most schools in NSW the trial HSC examinations occur in three weeks. Class assessment tasks have finished so we can now concentrate on studying. How can you best prepare for these examinations? First, you must have a study timetable, just like a daily school timetable where you have 60 minutes for each subject. Stick to the schedule. Have a 10 minute break between study sessions. Secondly, in your study sessions work through past examination questions by writing down answers on lined paper. Set out your work in an organised fashion so that this habit becomes automatic in examinations. Remember that perfect practice makes perfect. Here are some Physics revision questions:
What happens when a current flows through a conductor? In HSC Physics students learn that the resistance of a conductor is due to the collisions of the conduction electrons with the atoms in the conductor. These collisions transfer energy from the electrons to an increase in the vibrational energy of the atoms causing an increase in temperature of the conductor. What would be an estimate of the drift speed of conduction electrons through a metal; 1 mm/s, 1 m/s, 1000 m/s or 1,000,000 m/s? The answer is 1 mm/s. When a light globe is switched on an electric field is sent along the connecting wire at a speed of about one-third of the speed of light and this field pushes electrons at the far end of the wire through first, so the globe appears to glow immediately. Quantum mechanics also teaches us that electrons behave as waves. The electron waves are scattered by the irregularly spaced atoms in the conductor which are displaced from a regular pattern due to their thermal vibration.
Student's learn in HSC and IB Physics classes that the gravitational potential energy of two attracting masses is negative. Why is this? Let us consult the popular Physics textbooks to see what their authors say.
Resnick, Halliday and Walker Fundamentals of Physics (10th edition, page 365)...we choose a reference configuration with U equal to zero when the separation distance between the masses is infinite. The gravitational potential energy decreases when the separation decreases. Since U=0 for r=infinity, the potential energy is negative for any finite separation and becomes progressively more negative as the particles move closer together..
Serway and Jewett Physics for Scientists and Engineers (8th edition, page 386)...the potential energy is negative because the force is attractive and we have chosen the potential energy as zero when the particle separation is infinite. Because the force between the particles is attractive, an external agent must do positive work to increase the separation between the particles. The work done by the external agent produces an increase in potential energy as the two particles are separated.
Knight Physics for Scientists and Engineers (4th edition, page 366)...All a negative potential energy means is that the potential energy of the two masses at separation r is less than their potential energy at infinite separation.
Tipler and Mosca Physics for Scientists and Engineers (6th edition, page 374)....this means that U approaches zero as r approaches infinity. At first this may seem like a strange choice because for finite values of r all values of U are negative. This just means, however, that the potential energy is at a maximum when Earth and particle are at infinite separation.
Sears, Zemansky, Young, Freedman University Physics (14th edition, page 429)...in defining U we have chosen U to be zero when the body is infinitely far from the Earth. As the body moves towards the Earth, gravitational potential energy decreases and becomes negative.
Ohanian and Markert Physics for Engineers and Scientists (3rd edition, page 289)...the potential energy is always negative and its magnitude is inversely proportional to r. If the distance r is small, the potential energy is low (the potential energy is much below zero); if the distance r is large, the potential energy is higher (the potential energy is still negative but not so much below zero). Thus the potential energy increases with distance; it increases from a large negative value to a smaller negative value or to zero. Such an increase of potential energy with distance is characteristic of an attractive force. For instance, if we want to lift a communications satellite from a low initial orbit (just above the Earth's atmosphere) into a high final orbit (such as a geostationary orbit) we must do work on this satellite (by means of a rocket engine). The work we do while lifting the satellite increases the gravitational potential energy from a large negative value (much below zero) to a smaller negative value (not so much below zero).
With the trial examination period for 2017 quickly approaching it is important to talk about the best way to study Physics and Mathematics. The answer is to do questions. Questions may be from past exam papers or summary books. At this stage in schools new work should have been completed with a path of revision left towards the HSC. Write detailed answers to your questions. In Physics use the words clearly and make sure you answer the question that is asked. In Mathematics do not jump too many steps at once in your working as this is a very common source of error. Most importantly do not attempt at this stage to summarise or write out the text-book. This just takes up time and does not engage your brain to promote thinking and understanding.
A very common question in HSC Maths papers is to find the period of a given trig function. Some students regret putting the period of tan(x) as 2𝛑 in last year's HSC 2Unit paper! Here is a quick tutorial set on determining the period of trigonometric functions. Answers are given below.
[2𝛑, 2𝜋, 𝜋, 2𝜋, 2𝜋, 𝜋, 𝜋, 𝜋/2, 4𝜋, 2, 6𝜋, 2𝜋, 𝜋, 4𝜋, 2𝜋, 2𝜋]
Question 11 in IB Physics November 2016 Paper 1 was a question on determining the gradient of the V-T graph for an ideal gas. Only 11% of candidates answered this question correctly and this statistic is the lowest in SL papers in the last 4 years. Why was this question so difficult? The correct alternative, C, has the same form as the most chosen alternative, B . Alternative B contains the gas constant R whereas alternative C contains the Boltzmann constant k, which is correct; 66% of candidates sitting for the paper confused the constants by selecting alternative B. This could have been avoided by using the formulae on page 6 of the Data Booklet. Make use of the Data Booklet in Physics examinations.
Here are some points about the nature of cathode rays for HSC Physics.
Some facts about cathode rays.
Question 22 (SL) and Question 14 (HL) in the May 2016 IB Physics Paper 1 involved a mass on the end of a rod moving in a vertical circle in such a manner that the speed of the mass was constant. This question received the lowest percentage of correct responses in both papers and so it is worthwhile to discuss the Physics involved in this question. The question asks about the force exerted by the rod on the mass. The forces acting on the mass are its weight due to the Earth's gravitational field and the contact force of the rod pulling on the mass. Since the mass is moving at a constant speed in uniform circular motion the resultant force acting on the mass must always be directed towards the centre of the circle and must be constant in magnitude. As the mass moves around the circle the weight force is always directed downwards and so the direction of the contact force must change so that the vector sum of the weight force and the contact force is always directed towards the centre of the circle. At the top of the circle both forces point towards the centre of the circle and so the contact force has its minimum value at this position. Therefore the answer is D.
This is a phrase that often appears in student responses in Physics examinations. Let's look at various versions of it and see if they are correct. We will start from the most basic.
Here are some other misconceptions about the speed of light.
The speed of light in a vacuum is given the symbol c because c is the first letter of constant. Incorrect. The c comes from the Latin word celeritas for speed.
The Michelson and Morley experiment showed that the speed of light was always constant. Incorrect. There is no mention of the constancy of the speed of light in their paper describing the experiment. Einstein proposed this in 1905. M and M were not able to detect the motion of the Earth relative to the aether (this is a null result)
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In the May 2015 TZ1 IB Physics Paper 1 SL and HL there was a question (13SL,10HL) on the effect of damping on an oscillating system experiencing a driving force of variable frequency. The IB Examination Report states that "as damping is increased and friction is introduced into the system so the time per oscillation will increase, answer is B". This may not be intuitively obvious so a mathematical route to the solution may be helpful.
Let the frequency of vibration of the system when no damping occurs (usually just called the natural frequency) be F. The frequency of the driving force that acts on the system is f. The amplitude of the forced oscillations (this is the greatest displacement of the system from its equilibrium position) caused by the action of the driving force is A. Damping means that a resistive force is acting on the system as it vibrates causing its energy to decrease.
Driving force with no damping. When damping is not present a huge vibration known as resonance ocurs when the frequency of the disturbing force equals the natural frequency of vibration. As the amplitude is huge we can predict that the amplitude of oscillation must be inversely proportional to the difference in the frequencies. When f - F approaches zero A approaches infinity. A mathematical solution of the differential equation describing the system without damping gives A = 1/(f2-F2). How can a catastrophic vibration be avoided when f = F? Including a damping term in the equations removes some energy from the system allowing it to be unavailable to participate in a large vibration.
Driving force with damping. When a damping term is present the differential equation describing the system contains an additional term 2kv, where k is the damping coefficient and v is the velocity of the mass. The solution for A with damping is A = 1/√((f2-F2)2+ 4k2f2 ). Notice the additional term in the denominator. When f = F we have A = 1/(4k2f2) giving a finite amount of vibration when f = F. Catastrophe is avoided! Let us examine the equation
A = 1/√( (f2-F2)2+ 4k2f2 )
If we plot A versus f we obtain the graph shown on the 2015 examination paper. By differentiating A with respect to f we find that A has a maximum value of A0 when f has the value f0
f0 = √( F2-2k2 )
A0 =1/( 2k √(F2-k2) )
To answer the question, as k increases A0 decreases and f0 decreases so alternative B is the correct answer.
Welcome to Sydney Physics Tutor, my name is Stephen McAndrew. I have taught Physics and Mathematics in independent schools in Sydney and the UK for 38 years. I offer expert individual tutoring to allow students to fulfil their academic promise. I focus on the individual student and prepare structured work to address their particular deficiencies in knowledge and skills and develop these deficiencies into strengths. I use traditional methods of instruction where students write their answers in examination style format and are tested regularly to build their confidence and so develop a love of learning in Physics and Mathematics.
STEPHEN MCANDREW
MA, MSc, PhD, DipEd, CPhys, MInstP, MAIP, MAustMS, FRAS
Sydney Physics and Mathematics Tutor
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