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PHYS 212 Exam 1 Cheat Sheet.pdf

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PHYS 212
Nadya Mason

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PHYS 212- Spring 2014 Exam #1- Review Sheet General tip Becarefulaboutunits inElectromagnetism. Oftenprefixesareusedasthere aresmallorlargequantities. Always convert prefixes back to the base unit before using them mathematically. Sometimes you can find the correct choice by checking the signs/dimensions/limiting behavior. Vectors Vectors are shown by arrows. The length of arrow is proportional to the magnitude of vector. Vectors can be projected into their components ๐‘ฆ ๐ด ๐‘ฅ ๐ดcos๐œƒ ๐ดโƒ— ๐ด = ๐ดsin๐œƒ ๐‘ฆ ๐œƒ ๐‘ฅ Add vectors component by component: ๐ถ = ๐ด + ๐ตโƒ—โƒ— โ‡’ ๐ถ = ๐‘ฅ + ๐ต๐‘ฅ ๐‘ฅ ๐‘Ž๐‘›๐‘‘ ๐ถ๐‘ฆ= ๐ด +๐‘ฆ๐ต ๐‘ฆ Coulombโ€™s Law The electric force between two point charg1s ๐‘ž and2๐‘ž is given by ๐‘˜ ๐‘ž ๐‘ž 1 ๐‘๐‘š 2 ๐น = 1 2 ๐‘Ÿ12 ๐‘คโ„Ž๐‘’๐‘Ÿ๐‘’ ๐‘˜ = = 9 ร— 10 9 ๐‘Ÿ12 4๐œ‹๐œ– 0 ๐ถ2 Note that this has a similar form to the gravitation force between two masses, however, it can be either repulsive or attractive (like charges repel, unlike charges attract each other). Use superposition principle to compute the net force on charge q due1to 2 , ๐‘„ , โ€ฆ. ๐‘„ 1 ๐น3 ๐‘Ÿ1 ๐น2 โƒ—2 ๐‘„2 ๐‘ž โ‡’ ๐‘ž ๐น1 ๐‘„ โƒ—3 3 ๐‘˜ ๐‘„1๐‘ž ๐‘˜ ๐‘„ 2 ๐‘˜ ๐‘„ 3 ๐น ๐‘ก ๐น +1๐น + 2 = โƒ—3 2 ๐‘Ÿ1 + 2 ๐‘Ÿ2 + 2 ๐‘Ÿ3 ๐‘Ÿ1 ๐‘Ÿ2 ๐‘Ÿ3 Be careful here, you are adding vectors! Electric Field The electric field summarizes the influence of a collection of charges on any โ€œtest chargeโ€ q that we place in their vicinity. โƒ— ๐ธ = ๐น ๐‘ž And for the example above it is going to be ๐‘˜ ๐‘„ 1 ๐‘˜ ๐‘„2 ๐‘˜ ๐‘„3 ๐ธ = ๐ธ +1๐ธ + 2 = โƒ—3 2 1ฬ‚ + 2 ๐‘Ÿ2 + 2 ๐‘Ÿ3 ๐‘Ÿ1 2 3 Questions & Corrections: Hassan Shapourian ([email protected]) PHYS 212- Spring 2014 Exam #1- Review Sheet Notice that electric field is a property that we assign to the space surrounding a collection of charges. So, it doesnโ€™t โƒ—โƒ— depend on the test charge. Electric field is a vector field denotedโƒ—); i.e. it has magnitude and direction at every point of the space. Electric field lines: a graphical representation of ๐ธโƒ—) following these rules ๏‚ท Field lines originate from positive charges and end on negative charges ๏‚ท Field lines are continuous and never cross (except at the position of point charges) ๏‚ท The number of field lines connected to a charge is proportional to that chargeโ€™s magnitude. Important result of field lines representation: The electric field is stronger where the field lines are denser. Note that what matters is the density of field lines, being on a field line itself doesnโ€™t imply a stronger field! Mechanical Equilibrium A system is said to be in equilbirum where the net forcce on it vanishes. There are three types of equilibria: ๏‚ท Stable equilibrium: in this situation, once the system is slightly disturbed from equilibrium point, it experiences a restoring force and meets the equilibrium point periodically. Generally, this case can be demonstrated by a potential energy and force as in ๐‘ˆ(๐‘ฅ) ๐น(๐‘ฅ) ๐‘ฅ ๐‘ฅ ๏‚ท Unstable equilibrium: here, if the system is disturbed, it moves away from the equilibrium point. Not only is there no restoring force, but also the force tends to push the particle away. ๐‘ˆ(๐‘ฅ) ๐น(๐‘ฅ) ๐‘ฅ ๐‘ฅ ๏‚ท Indifferent equilibrium: the system is indifferent to any perturbation. ๐‘ˆ(๐‘ฅ) ๐‘ฅ The fastest way to determine the type of equilibrium is to displace the particle from it equilibirum position and find the dominant force. Gaussโ€™ Law Electric flux: the total field strength passing through a given surface. In a fluidic system, it would be net amount of fluid passing through a surface per unit time. ฮฆ = โˆซ๐ธ.๐‘‘๐ด = โˆซ๐ธ cos๐œƒ ๐‘‘๐ด Questions & Corrections: Hassan Shapourian ([email protected]) PHYS 212- Spring 2014 Exam #1- Review Sheet where ๐‘‘๐ด is directed normal to the element of area ๐‘‘๐ด with magnitude equal to area of that element. In case of uniform field on flat surface, it is simplified into ฮฆ = ๐ธ๐ดcos๐œƒ. Statement of Gaussโ€™ law: the total electric flux through any closed surface is propotional to the total amount of charge enclosed by that surface. ๐‘„ ๐‘’๐‘›๐‘ ฮฆ = โˆฎ๐ธ.๐‘‘๐ด =โƒ— ๐œ– 0 Note that ๐‘‘๐ด is always directed outward for a closed surface. Application of Gaussโ€™ law: We can use Gaussโ€™ law to compute the electric field for some symmetric chage distributions. Here is a four-step procedure to do this: ๏‚ท Sketch the electric field lines using all the symmetries of the problem. ๏‚ท Choose a suitable Gaussian surface based on the geometry of the problem. ๏‚ท Determine the total charge enclosed by your surface. ๏‚ท Evaluate the flux integral and combine it with Gaussโ€™ law to dete๐ธ.ine Ex
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