Tips from a Physics Tutor Geometric Intuition, Part II - Symmetry

Welcome back to our series of posts of using our physical intuition in E+M! We’re focusing today on how you can easily intuit the direction of an electric or magnetic field created by some arrangement of charges or magnetic fields. This skill, of looking at a problem and using logic and physical reasoning to figure out with a good deal of certainty what the answer must be, will make your experience with high school or college physics courses easier and is indispensable for taking the physics SAT II or physics GRE. Let me say here that physical intuition is a powerful tool in any scientist’s toolkit, but it is no substitute for knowing how to work through the mathematical nitty gritty of the problem. Intuition lets you bypass the math in many cases, but you should always know how you would do the calculation. For example, you can use the intuitive techniques from the past two lectures to know that the magnetic field caused by an infinite wire wraps around the wire and falls off as 1/r. That is true and useful – you can picture the system in your mind and answer many multiple-choice questions knowing only this – but you would need to do the math to calculate the actual magnitude of the field at some given distance. Think about geometry, and symmetry There are two methods you can use to intuit the direction of an electric or magnetic field. First, as we discussed in the last post, look at the collection of charges and currents and think about how its direction is defined. For example, if you have an infinite sheet of charge, you can define the orientation of that sheet by giving the direction of a vector perpendicular to the surface. It makes sense, then, that the electric field points along that vector, either straight out of or straight into the sheet of charge. But let’s play devil’s advocate with this method a bit, and you’ll see how the second method – examining the symmetry of the collection of charges or currents – becomes very useful. Let’s say you have an infinite line of charge. Two students, Alice and Bob, look at the problem and come to two different conclusions. Alice states that we should define the direction of the wire by taking the vector from the wire to our observation point, so the field should point radially outward from the wire. Bob, however, says that the direction of the wire is plainly defined by a vector pointing parallel to the wire, so the field should also run parallel to the wire. Who is right, and how can we tell? Should we compromise and just take the cross-product of the two vectors? Move the problem around in your mind Let’s examine the symmetry of the infinite wire, which we can imagine runs horizontally from left to right. That is, how can we move our observation point relative to the wire so that, from the observation point, the wire looks exactly as it does now? First, let’s try sliding the point horizontally to the left or right. Being an infinite wire, the situation looks exactly the same; the wire still extends infinitely far to both the left and right. This is translational symmetry under translation (linear movement) to the left or right. Next, let’s try rotating the point around an axis running through the wire’s center. The wire is assumed to be infinitesimally thin, so it looks the same from all sides. This is rotational symmetry under rotation around the wire’s axis. All symmetries give information; find the symmetry that gives the information you need Those facts make sense, and might seem uninterestingly obvious to you, but what do they tell us about the electric field? The translational symmetry says that there is no special point along the wire: the electric field 5 cm above the portion of wire directly in front of you is exactly the same, in magnitude and direction, as the field directly above a portion of wire 500 miles to your right. The rotational symmetry says that there is no special direction around the wire: the field 5 cm above the wire has the exact same magnitude as the field 5 cm below the wire. We must be careful about the direction, though. We use the fact that the wire has rotational symmetry to prove that the field also has rotational symmetry relative to the wire. That is, we can’t say that if the field above points up/down/left/right/front/back, then the field below also points up/down/etc. We have to say that if the field above points radially toward/radially away from/clockwise around/counter-clockwise around/along the wire to the right/along the wire to the left, then the field below does also. These are useful truths, but they don’t help us decide between Alice’s interpretation and Bob’s. The field could point along the wire, around the wire, or radially away from the wire at all points in space and still satisfy those two conditions. Is there another symmetry we can use? What if we step to the other side of the wire and then look at it from the observation point? From our point of view, the wire that was coming in from the right is now coming in from the left. Remember that there is no motion or current here, only static charge, so the situation still looks identical. The field must also look exactly the same, so we can decisively rule out the cases where the field wraps around or runs along the wire. Alice must be right: the field points radially outward from the wire at all points. This symmetry brings up a fatal flaw in Bob’s argument: he says that we should define the wire by a vector pointing along it, but â€Å"along† it in which direction? Should the field point to the left or right? There’s no physical reason for it to choose one option and it can’t do both, so it must do neither and point straight outward. How are magnetic fields different? This reasoning works for electric fields, but what about magnetic fields? What if the wire were not carrying a static charge, but a flowing current? The first two symmetries – translational symmetry along and rotational symmetry around the wire’s axis – still apply, so the first two conclusions hold. Wherever the magnetic field points, the direction is the same both along and around the wire. What about the third symmetry? When we stepped to the other side of the charged wire, it looked the same, so we also wanted the electric field to look the same. When we do the same to the current-carrying wire, the apparent direction of the current reverses! If current was flowing from left to right, it is now flowing from right to left. Therefore, the direction of the magnetic field should also be reversed under this rotation. That means that the field either wraps around the wire or runs parallel to it. Now we see that reasoning with symmetry isn’t perfect either; we can’t make a symmetry argument that tells us which of these two choices is correct. Use symmetry and geometry together! This illustrates the overarching point of these two posts: you need to consider both the geometry and symmetry in the problem to make an informed intuitive decision. We saw in the last post, and we can recall from our discussion of the Biot-Savart law, that you usually can find the direction of a magnetic field caused by some current by taking the cross-product of the current’s direction and the vector from the current to the observation point. Because the current flows along the wire, and c is always perpendicular to a and b if c = a x b, then we see that the field cannot also point parallel to the wire. Therefore, we reach the same conclusion that we reached last time, and that you’ve doubtlessly reached in class: the magnetic field caused by a current-carrying wire wraps around the wire. Solving the mystery from last time At the end of the last post, we used the example of a ring of charge to illustrate how considering the geometry of a problem alone is sometimes insufficient. Imagine you have a ring of charge, an electrified donut, and you need to find the electric field in the center of the hole. For concreteness, let’s say that the charge is positive and the ring is lying on a horizontal table. The donut’s orientation is defined by the vertical axis pointing vertically up through the center of its hole. Rotational symmetry also confirms this; there is no special point along the outside of the donut, so why would the field choose to point in any particular horizontal direction? Now, does the field point up or down? Exactly as with the charged wire, we can choose to look up at the ring from the center or down at the ring from its center. Since the ring looks identical from either perspective, the field must also look identical from either perspective, neither up nor down. Since symmetry prevents the field from pointing up, down, or to the side in any direction, we conclude that the field must be exactly zero at the center of the ring! This makes sense; the field from any bit of charge is exactly canceled by the field from a bit of charge on the other side of the ring, leaving zero net field. Notice, however, that this argument does not mean that a point slightly above or below the center of the hole must have zero net field. The ring looks identical if we look down on it from a point above the center or up at it from a point below the center. This implies that if the field points up above the center then it must point down below the center, or vice versa. Unlike the case where we were looking up and down at the ring from the same point, at the center, this is perfectly possible. Symmetry can give us a complete picture of what’s going on! If the ring is positively charged, then the field points up above the center, down below the center, and is zero at the center. Build your intuition – use geometry and symmetry By thinking both about the geometry and the symmetry in a problem, you can use your physical intuition to draw some powerful conclusions about the problem’s solution. Think of this approach in analogy with the technique of dimensional analysis. You need to look at the numbers or vectors given to you in the problem. You also need to manipulate them so that the numbers’ units or the vectors’ symmetry properties behave the way logic says they should. If you work on building up this intuition, physics will become much easier and more fun for you! ;

The Amendment Of The Voting Rights Act - 936 Words

Thus, when faced with arbitrary legislative action or inaction, judicial intervention â€Å"is not only appropriate but essential† to protect citizens’ constitutional rights. Furthermore, when the Court resolves constitutional questions that, for whatever reasons, elected representatives, cannot, its rulings can guide lower courts, legislators, and citizens concerning the scope of individual rights and permissibility of governmental conduct. When the Court applies the standing doctrine regardless of legislative inertia or entrenchment, some citizens are left with rights but no remedies and a government that is unaccountable and unresponsive to its citizens. This was precisely the point that Justice Scalia made in Shelby County, and most likely why the Court refused to defer to Congress despite overwhelming support for re-authorization of the Voting Rights Act. Noting that â€Å"they [Senators] are going to lose votes if they do not reenact the Voting Rights Act,† and suggesting that the Act would be â€Å"reenacted in perpetuity unless †¦ unless a court can say it does not comport with the Constitution,† Justice Scalia recognized the necessity for judicial intervention in this situation. The same principle should be applied when politically powerless citizens seek to challenge the constitutionality of law and redress through the democratic process is nothing but an exercise in futility. To deny such citizens standing where they assert a legally cognizable harm, are within theShow MoreRelatedThe Social Problem Of Voting Rights1668 Words   |  7 PagesThe social problem: What is the social problem you will examin e? The research will examine voting rights in relation to voting right inequalities and the society’s effort to have an all minority groups included in the civic process. 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Formalistic Approach to Ozymandius Essay - 828 Words

Formalistic Approach to Ozymandiusnbsp;nbsp; nbsp; While analyzing a poem, a reader notices many things, things like rhyme scheme, word choice, different levels of a poem, and sentence structure. Each one of these things is an ingredient for the four main components of the formalistic approach to poetry. In the poem Ozymandius by P.B. Shelley, structure, style, form, and imagery, allow the reader to look deeper into the poem. nbsp; First the reader must look at the structure of the poem. However, the structure of Ozymandius is difficult to understand. With no set pattern or rhyme scheme, one must truly study the poem to notice particular things that stick out. At first, one notices the randomness of the rhyme scheme,†¦show more content†¦After reading the description, the reader finally arrives at the third and final level of the poem, Ozymandius himself. At this level, the reader actually feels the presence of Ozymandius. After hearing direct words from Ozymandius, the reader has now experienced all three levels of the poem. nbsp; The second component of formalistically analysis of this poem is looking at style. The most obvious stylistic component of the poem is that it serves as a narrative poem. It tells a story using a hermeneutic circle. In its first level, the traveler tells about a sculptor and his statue. In the second level, the sculptor describes both the rule of Ozymandius and his personal feelings about it; and in the third level, Ozymandius explains to the people around him how great and powerful he sees himself. Thus, throughout all three of the levels in the poem the reader discovers a new story, which affects the other stories A second item the reader looks at is sentence structure. In Ozymandius, three complex sentences stretch throughout all fourteen lines. Though each sentence is complex, the second sentence contains most of the information because it continues for nine lines. Within this sentence, one can see the only example of alliteration in the poem: cold command, and this example helps stress the importance of the sculptors statue. Making up the

Sustainable Hospitality and the Current Status

Question: Write a report on rapid growth of the hospitality industry and the current status of the environmental conditions, implementation of the environmental sustainability practices. Answer: Introduction The report outlines the methods adopted by the hotel in their business for attaining sustainability. It highlights the impacts of sustainability and also describes the need for sustainability in hospitality management. Over the past few years, it can be observed that the hoteliers are focusing on the practices for enabling sustainability and sustainable practices in the hotel environment. The hospitality management is putting emphasis on the importance and development of sustainability in the hotel as it is directly correlated with the hospital development and its operations. Sustainable issues are among one of the various problems faced in todays world in all the businesses. Need of sustainability The hospitality sectors are putting more focus on the strategies that will help in ensuring sustainability in their working environment. There are lots of chances of enhancing sustainable business strategies and pollution free workplaces. The dramatic negative impact on the environment has been seen through energy and water consumption, use of consumable goods and overuse of products, and also the accumulation of solid and waste hazardous excretions. Hotels are more relying on consumption of energy for HVAC operations, in lighting, fuel, and other power uses. Overuse of water in bathrooms, laundry, and other general purposes. Waste products are more and more generated by the disposal of paper, equipment, batteries and other more. The hoteliers realize that guest experience can be enhanced by integrating some of the natural elements that will generate the evolution of green thoughts in the community. There are certain factors that could be done to maintain the concepts of sustainabili ty in a hotel environment. The benefits of accepting sustainability are- reduction in costs, economic incentives, regulatory affairs, guests feelings, corporate brand identity and publicity of brand image. Strategies adopted for sustainability To explore sustainable practices, the companies need to adopt the strategies and methods which can enable sustainability in hotels. There are many hotels which have already adapted steps for sustainable management in their environment. The cities of Europe and Asia have shifted their attitudes towards sustainability. Earlier, the whole of the market used to focus on consumerism; that means they were emphasizing on the best ways of serving customers (Prudhomme and Raymond, 2013). But now the business marketing and their strategy are shifting towards focusing on sustainable and environmental factors that would enable sustainability. The major problems that sustainable development is generally facing today are- changes in climate, pollution, erosion, biodiversity loss, the abundance of resources and water cleanliness. It can be said that in a working environment, the ability of the organization to conduct business in a way that can help in minimizing pollution and appraises careful use of natural resources is termed as sustainability. Evidences of sustainability management practices The sustainability specialist, Briton John Elkington in 1997, put forward the concept of the triple bottom line. According to this, for attaining full sustainability bottom line performance along with social and environmental performance need to be achieved. Among many of the hotels present in the United States, the company Destination Earth has developed certain methods which they follow for attaining sustainability (Xu and Gursoy, 2015). They have developed green teams who work in carrying out the sustainability programs in all their hotels and resorts around the country. They have made partnerships with environmental consultants and had introduced certain customized initiatives for encouraging environmental sustainability. There are many benefits of choosing environmentally sustainable methods. The profits are- customer loyalty, employee retention, awards and recognition, risk management, increased brand value and regulatory compliance. By the use of the methods that can help in s aving energy, water, and other renewable sources, sustainability can be achieved. Methods adopted for sustainability There are certain steps by following which a hotel can attain sustainability (Legrand et al, 2012). The operational principles are related to the concepts of what to do and how to do business in daily life practices. The operational principles are- good employer, environmental responsibility, community contribution and fairness and also influencing others. The interaction between the principles of economic growth, social equity, and environmental protection can help in producing a sustainable system (Binder and Varga, 2015). In hotels, the formulation of new policies and procedures, management of control systems and human resources practices can also help in achieving sustainability. The cost savings, fiscal and regulatory incentives, regulatory affairs, stabilized utility prices and their availability, guest experience, marketing image, employee retention and investor requirements. Zero-energy housing follows the ways that help in the reduction of energy consumption for heating room (Melissen 2013). The use of an appropriate mechanical ventilation system and using the used air, which is evolving out from technical functions can help in heating rooms. Use of low energy light bulbs and LEDs can help in saving energy. Recently developed automatic key card systems are installed in the rooms of hotels for energy consumption by people, and they are shut when they are not in the room (Deale 2015). For reducing the water usage and the consumption rate, the water distribution profile of hotel should be determined. Guests in the hotels use water at a great rate, so it needs to be minimized for saving water resources. Using water efficient showerheads and rainwater for washing purposes can help in overwhelming the problems. Installation of aerators and flow restrictors can be a highly efficient method or serves as a low budget solution for solving the problems of over-consumption of energy. Most of the hotels have taken initiatives for recycling and reduction of waste materials (Jones et al, 2016). The three Rs reduce, reuse and recycle of the highest priority in the hospitality industry. It can be observed that paper and composed beverages are the causes of over 65% of all the hotel wastes while 95% of it can be reused by recycling them. The most accepted form of renewable energy in the hospitality industry is using the sun as energy providers (Ali et al, 2016). According to the carbon trust organization, more than of the UK workers have been using active policies to minimize carbon emissions and are agreeing to avoid the usage of maximum energy as resources. Green practices in the hospitality industry require measurement of carbon emission which is estimated by HCMI. HCMI stands for hotel carbon measurement initiative (Chan and Hsu, 2016). This is found to be an effort for determining the carbon emissions from rooms of the hotels. This serves to be the first and simplest steps adopted by many hotels towards sustainability. This estimation helped in comparison of the basic sustainability of the hotels globally and also lets makes decisions of how to invest money and at what rates. The hotels can also move towards sustainability by recycling of non- hazardous wastes. Recycling of wastes like cardboard, cups, plastics, household wastes and much more can help in attaining sustainability (Lim 2016). The use of green products in hotels can help in minimizing the negative impacts of the products in environmental. The green products are less non- toxic, less- processed, recyclable and biodegradable and so their use can help in reduction in consu mption of water and energy. On the other hand, apart from adopting all these methods, educating employees and making them aware is one of the important things to be considered for creating sustainability (Prud'homme and Raymond, 2016). Current energy technologies have been contributing to create serious environmental problems. The world is facing problems of extinction of fossil fuels and the transition to renewable energy resources is required. Benefits of sustainable practices There are several benefits of adopting sustainable management in the workplace. The benefits are- cost savings, competitive advantage, employee retention, customer loyalty, regulatory compliance and risk management (Jones et al, 2016). Many hotels have used social initiatives and corporate social responsibility for attaining sustainability. Corporate social responsibility involves promoting and practicing environmental initiatives (Fermani et al, 2016). Hotels sustainability practices are important for saving energy and resources. Many of the environmental regulations today are targeting on facility activities like management of storm water, removal of harmful substances and health and safety of the environment. Guest experiences are influenced significantly when the hotels adopt the practice of sustainability. Using sustainable practices helps in maintaining the brand image of the hotel. Conclusion With the rapid growth of the hospitality industry and the current status of the environmental conditions, implementation of the environmental sustainability practices within the hospitality industries is important for preservation of the natural resources and the victory of the industry. Gaining knowledge about the methods that can maintain sustainability can help in improving the industrys fame and dignity. Sustainable practices in the hospitality industry have been found to have profound growth as because the managers are getting more aware of the benefits arising due to the adoption of sustainability. All the hospitals should adopt the practice of sustainability for the betterment of the environment and people too. Reference Ali, A., Murphy, H.C. and Nadkarni, S., 2016. Hospitality employers perceptions of technology for sustainable development: The implications for graduate employability.Tourism and Hospitality Research, p.1467358416636929. Binder, A. and Varga, P., 2015. Sociocultural hurdles of sustainable hospitality management.Asia-Pacific Journal of Innovation in Hospitality and Tourism,4(1), pp.77-92. Chan, E.S. and Hsu, C.H., 2016. Environmental management research in hospitality.International Journal of Contemporary Hospitality Management,28(5). Deale, C.S., 2015. Entrepreneurship and Sustainability in Hospitality and Tourism: Implications for Education and Practice. Fermani, A., Crespi, I. and Stara, F., 2016. Sustainable hospitality and tourism at different ages: Womens and mens attitudes in Italy.Research in Hospitality Management,6(1). Jones, P., Hillier, D. and Comfort, D., 2016. Sustainability in the hospitality industry: some personal reflections on corporate challenges and research agendas.International Journal of Contemporary Hospitality Management,28(1). Legrand, W., Simons-Kaufmann, C. and Sloan, P., 2012.Sustainable Hospitality and Tourism as Motors for Development: Case studies from developing regions of the world. Routledge. Lim, W.M., 2016. Creativity and sustainability in hospitality and tourism.Tourism Management Perspectives,18, pp.161-167. Melissen, F., 2013. Sustainable hospitality: a meaningful notion?.Journal of sustainable Tourism,21(6), pp.810-824. Prudhomme, B. and Raymond, L., 2013. Sustainable development practices in the hospitality industry: An empirical study of their impact on customer satisfaction and intentions.International Journal of Hospitality Management,34, pp.116-126. Prud'homme, B. and Raymond, L., 2016. Implementation of sustainable development practices in the hospitality industry: A case study of five Canadian hotels.International Journal of Contemporary Hospitality Management,28(3). Xu, X. and Gursoy, D., 2015. Influence of sustainable hospitality supply chain management on customers attitudes and behaviors.International Journal of Hospitality Management,49, pp.105-116.

Essay Topic Ideas - How to Write Great Essay Topics

Essay Topic Ideas - How to Write Great Essay TopicsMany people take a great deal of pride in writing a good English essay topic. There are so many ways to turn around your poor topic choice and make your essay more interesting. Here are some tips to help you increase the number of your topics in your essay. These are just basic guidelines that you can use to increase the number of your essays.One of the most common mistakes that students make is to choose a topic that they don't understand well. It's very easy to get lost in the weeds when it comes to reading through your papers, even if you're the best English student in the world. I can't tell you how many times I've seen a perfect essay topic get destroyed because of a poorly chosen one. By choosing a topic that you do not understand, you're risking making your essay goes down in flames. So, if you've ever wondered why so many students fail at essay topics, this may be the cause.It's always easier to find an interesting topic than it is to write an excellent one. Look up some of the things that interest you and think about a time when you were curious about something. Maybe you were curious about how to write a book, or how to become the next president. You may have even enjoyed learning more about a subject and decided to write a topic about it.The trick to writing a good topic is to find something that interests you. If you're really interested in something, that will get you going on topics that are more interesting than others. With this in mind, you may want to avoid picking topics that are boring or don't seem interesting to you.The second tip is to decide on a topic early. Start writing an essay that you want to have finished by the end of the year. Try to come up with a topic that will be ready to get accepted by your instructor at the beginning of your senior year. Once you've decided on a topic, start writing. Write as many essay topics as you can and then turn them in.Your great teacher once told me that you must prepare your topic before you write it. Don't just jump into it; sit down and write a few words about what it is that you want to say. This will give you ideas about how your topic should go.These are just some of the basic things that you need to know about writing English essay topics. Make sure that you practice writing for a while before you write an essay. It's important that you enjoy doing it, otherwise you may not enjoy the results of your work.

The Good, the Bad and Ielts Essay Samples Band 4

The Good, the Bad and Ielts Essay Samples Band 4 Ielts Essay Samples Band 4 - Is it a Scam? Every year, an increasing number of people from all around the world choose to leave their home countries and move to some other place. After discovering our website, you will no longer will need to bother friends and family with these kinds of requests. For instance, people are able to access news, medical advice, online education courses and far more via the web. Students lead busy lives and frequently forget about a coming deadline. There's, clearly, a limit on the range of pages even our finest writers can produce with a pressing deadline, but usually, we figure out how to satisfy all the clients seeking urgent assistance. As computers are getting to be a standard tool for teaching, teachers need to be more conscious of their job as guides in the acquisition of knowledge in place of transmitters of facts. 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Essay Examples For College Admissions

Essay Examples For College AdmissionsAdmission essays are one of the most important parts of an application. As such, essay samples for college entrance exams should be carefully chosen to accurately reflect the student's abilities and interests. Selecting the right essay sample is an important part of the application process, because it will provide a unique perspective that the admissions officer will use to make a decision about the student's talents.There are several places that students can purchase essay samples for college admission. The most popular course of action is to go online and download samples directly from the schools they are applying to. This is certainly the easiest way to get them, but it is also the least effective way. It is important to know the specific policies and procedures of each school before downloading essay samples for college admission.Most school's website has a 'sample' section in which you can upload your own essay. If your college website offer s a specific selection of essays, it is important to study them closely. Each essay on the list should be assessed based on the topics that are covered in that particular essay.Some students would rather look at admission essay samples for college admission on television. Several programs feature the school essays that will be read during the admission interview. These programs feature a variety of students writing samples. It is important to remember that they are not all likely to write well, and you may want to spend some time editing and improving your essay before submitting it.You can also find many admission essay samples for college admission by visiting libraries. Most public libraries have large stacks of papers that have been donated by students who need help choosing a college. These papers can be extremely helpful to students in figuring out what schools are good for them.When considering essays, it is very important to take time to read essay samples for college admiss ion that come with lots of examples. The majority of these articles will focus on topics that students will face while attending college. The rules for college will be different for everyone and this is why writing a personal essay is so difficult. Essays that focus on the same topics in different ways may sound redundant or even confusing.While researching essays for college admission, it is a good idea to consider what books were used by the authors of many of the classics of our modern literature. While reading these books and essays, try to imagine how they might apply to your life when you are trying to decide what college to attend. This is something that can only be done with a great deal of research and consideration.Your college essay is a chance to shine as a potential applicant. You will want to take the time to choose the best essay samples for college admission that will not only highlight your uniqueness, but also help you stand out from the crowd. Spending some time r esearching the topics that will be covered in your essay is a great way to make sure that you choose a personal essay that is not only informative, but also fun.