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# Elec Magnetism & Light PHYS 241

Community College of Philadelphia

GPA 3.82

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This 11 page Class Notes was uploaded by Ms. Allie Wisoky on Sunday October 11, 2015. The Class Notes belongs to PHYS 241 at Community College of Philadelphia taught by David Cattell in Fall. Since its upload, it has received 28 views. For similar materials see /class/221233/phys-241-community-college-of-philadelphia in Physics 2 at Community College of Philadelphia.

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Date Created: 10/11/15

PHYS 2411 Notes for Test 5 Chapter 30 Induction and Inductance Review and Summary is on p 816 Know the de nition of magnetic ux Equation 301 Know Faraday39s law of induction Equations 304 and 305 Be able to state Lenz39s law An induced current has a direction such that the magnetic eld due to the current opposes the change in the magnetic ux that induces the current The induced emf has the same direction as the induced current Know that a changing magnetic eld produces an electric eld in accordance with Faraday s law as written in Equation 3020 this is one of Maxwell 393 Equations Know the de nition of inductance Equation 3028 and the de nition of its unit the henry Know what self induction is and the formula for the selfinduced emf in a coil Equation 3035 gL Ldidt Note that the minus sign is an expression of Lenz39s law RL Circuits Know how to use Kirchhoff39s loop rule and Equation 3035 to write the differential equation for the current in an RL circuit Know how to derive Equation 3041 for the rise of current in an RL circuit Know how to derive Equation 3045 for the decay of current in an RL circuit Know equation 3049 for the magnetic energy U B stored in the magnetic eld of an inductor U Li2 B where L is the inductance of the inductor and i the current passing through it Note the similarity with the equation for the electric energy stored in the electric eld of a capacitor 2 1q U7i E 2C Continued on the other side Chapter 31 Electromagnetic Oscillations and Alternating Current Review and Summary is on p 853 In a resistanceless and undriven oscillating LC circuit you should know that at each instant the energy stored in the capacitor is UE q22C and the energy stored in the inductor is UL LizZ UE UL is a constant You should know how to use the loop rule to derive Eq 3111 You should know that the solution of this equation is given by Eq 3112 a Qcosoat 1 where n f Given initial conditions you should know how to nd the phase constant I Also know how to nd the current i as a function of time You should also know that if V is the voltage across the capacitor then a CV In an undriven RLC circuit you should know how to use the loop rule to derive Eq 3124 It is not necessary to remember the mathematical form of the solution but you should know what its graph looks like if n gt IUZL You should know that this is called damped oscillation You should know that for forced oscillations where the driving voltage is given by Smsinndt electrical l resonance occurs when n f LC You should know that a driven RLC circuit where the voltage is given by Smsinoa dt has both a transient and a steady state response The form of the steady state current is i Isinnt 1 You should know the formulas for inductive reactance XL 03L and capacitive reactance X c lnC You should know that the voltage and current amplitudes are related by V IZ where for a series RLC circuit Z XL Xc2 R2 and that the phase constant is given by tan You should know that for a purely inductive load the voltage leads the current by 90 that for a purely capacitive load the voltage lags the current by 900 and that for a resistive load the current and voltage are in phase You should know how to represent these facts in a phasor diagram You should be able to use such a diagram to derive the formulas for Z and tan given above Continued on the next page You should know how to nd rms rootmeansquare values of current and voltage Irms 0707 Vms 0707V where I and Vare the current and voltage amplitudes respectively You should know that the average power dissipated by the resistor in an RLC series circuit is given by Pav ImszR Vmstmscosq where coscl is called the power factor of the circuit Know the basic principles of operation of a transformer Know what is meant by the primary winding and the secondary winding Know that 1pr 15Vs Continued on the other side Chapter 32 Magnetism of Matter Maxwell s Equations Extra Credit N Be able to work out a problem involving induced magnetic elds and displacement currents such as problems 3217 and 3218 in the text State and identify by name all four Maxwell equations Be able to identify all the symbols in each formula See Table 321 on page 868 ofyour text PHYS 241 Notes for Test 6 Chapter 33 Electromagnetic Waves Review and Summary is on p 913 Know what is meant by an electromagnetic plane wave Know that for this wave the electric and magnetic eld vectors are in phase and that E x B points in the direction of propagation of the wave See Figure 335 Know that if this wave is traveling in the direction of the xaXis the magnitudes of the electric and magnetic eld vectors at position x and time t are given by E Emsinkx oat B Bmsinkx oat If 7 and f are the wavelength and frequency respectively k 211 is the wave number of the wave and n 21tf is the angular frequency of the wave Remember these results from Physics 140 0 and c nk where c is the speed of light 0 300 X 10 ms in a vacuum Maxwell s equations predict the speed of l V 080 The rate per unit area at which energy is transported via an electromagnetic wave is given by the Poynting vector g in Equation 3319 electromagnetic radiation in a vacuum to be c Also at any given instant c E s7 Li X E Ho For an electromagnetic wave the timeaveraged rate per unit area at which electromagnetic energy is transported Savg is called the intensity I of the wave Know Equation 3327 for a point source of power PS that emits electromagnetic radiation isotropically the intensity a distance r from the source is given by P s 411r2 When a surface intercepts electromagnetic radiation a force and a pressure are exerted on the surface If radiation of intensity I is totally absorbed by a surface the pressure is given by Equation 3334 p i total absorption c if the radiation is totally re ected the pressure is given by Equation 3335 2I p i total re ectlon back along path c Know the meaning of the term polarization and what polarizing sheets are Know that if unpolarized light passes through a polarizing sheet the transmitted intensity I is half the original intensity I 0 as given in Equation 3336 Continued on the other side Know that if polarized light passes through a polarizing sheet the transmitted intensity I is related to the original intensity I 0 by Malus law Equation 3338 I 10 cosze where 9 is the angle between the polarization direction of the original light and the polarizing direction of the sheet Know the de nition of geometrical optics and when geometrical optics is applicable Geometrical Optics is an approximate treatment of light in which the paths taken by light waves are represented as straight line rays Geometrical optics is applicable when the dimensions of the objects the light encounters are much larger than the wavelength of the light Know what re ection and refraction are the law of re ection Equation 3339 and the law of refraction Equation 3340 also known as Snell s law n2 s1n 92 nl s1n 91 where n1 and n are the indices of refraction of the media in which the incident and refracted light rays travel 91 is the angle of incidence and 92 is the angle of refraction Know that the index of refraction of a medium is the ratio of the speed of light in a vacuum to the speed of light in the medium n cv Know what total internal re ection is what the critical angle is and how to derive Equation 3344 for the critical angle 95 sin391 E where n1 and n are the indices of refraction of the media which form the boundary on which the light is incident Light is incident in medium 1 and for total internal re ection we must have nl gt n2 light is trying to pass from a slow to a fast medium Polarization by Re ection Know that a re ected wave will be fully polarized with its E vectors perpendicular to the plane of incidence if it strikes a boundary at the Brewster angle GB given by Equation 33 n SE tan391 2 quot1 Also know that the refracted ray if it exists makes a right angle with the re ected ray in this case Know how to use this fact to derive equation 3349 Continued on the next page Chapter 34 Images Review and Summary is on p 947 Know how images are formed by plane mirrors spherical mirrors and lenses Know the de nition of a real image and the de nition of a virtual image Know that paraxial rays are rays that make a small angle with respect to an optic axis Know the following symbols and sign conventions p object distance assume p gt 0 unless told otherwise a image distance a gt 0 for a real image and q lt 0 for a vi1tual image h object height assume h gt 0 unless told otherwise h image height h39 gt 0 for an upright image and h39 lt 0 for an inve1ted image f focal length f gt 0 for a converging lens or a concave mirror f lt 0 for a diverging lens or a convex mirror For a mirror f r where r is the radius of curvature of the mirror r gt 0 for a concave mirror and r lt 0 for a convex mirror Know that the magni cation of an image is de ned as hi m 7 h and for paraxial rays can be found from equation 346 i m i P for both mirrors and thin lenses Know that for paraxial rays the following relationship holds for both mirrors and thin lenses Know that when applied to lenses this formula is known as the thin lens equation Know how to draw a ray diagram to locate an image for an optical system as you did in Experiment LO3 PHYS 241 Notes for Test 1 Chapter 21 Electric Charge Review and Summary is on p 573 You should know the facts stated in the two paragraphs under the heading Electric Charge in the Review and Summary You should know Coulomb s law Eq 214 2 You should know that 1 899 gtlt109 N m 411780 C2 You should know how to nd the magnitude and direction of the resultant force on a given charge due to a number ofpoint source charges See Sample Problem 212 on p 569 and the example we did in class You should know that charge is quantized and that the elementary smallest charge is e 160 X 10 19C You should know that charge is conserved the net charge of any isolated or closed system cannot change Chapter 22 Electric Fields Review and Summary is on p 596 You should know the de nition of the electric eld and the concept of electric eld lines You should know how to calculate the electric eld of a point charge Eq 223 You should know how to nd the resultant electric eld due to a number of point source charges You should be able to express this electric eld in i j notation and be able to nd its magnitude and direction See the example we did in class You should know how to nd the force on a point charge in an electric eld Eq 2228 You should know the charge con guration of an electric dipole and the de nition of the electric dipole moment p You should know how to nd the electric eld due to a continuous charge distribution using integration See Sample Problem 223 on p 588 homework problem 2232 and the example we did in class Also read the Problem Solving Tactics A Field Guide for Lines of Charge on page 589 You should know how to nd the torque on an electric dipole in an electric eld Eq 2234 You should know how to nd the potential energy of an electric dipole in an electric eld Eq 2238 See Section 38 on pp 4849 of your text for a review of vector multiplication Continued on the other side Chapter 23 Gauss Law Review and Summary is on p 620 You should know how to calculate the net electric ux through a closed surface using Eq 234 You should know Gauss law Eq 236 You should be able to explain why at electrostatic equilibrium the electric eld inside a charged conductor is zero You should know how to use Gauss law to show that at electrostatic equilibrium all excess charge resides on an electrical conductor s outside surface You should know how to use Gauss law to show that just outside a charged conductor E 380 where 6 is the surface charge density of the conductor at the point where the electric field E is determined You should know how to use Gauss law to find the electric field intensity due to a charge distribution that has a high degree of symmetry See Problem Solving Tactics on p 612 Using Gauss law you should be able to derive Eq 2311 for E just outside a charged conductor Eq 2312 for E outside an infinite uniform line of charge Eq 2313 for E outside an infinite uniform sheet of charge Eqs 2315 and 2316 forE outside and inside a uniform shell of charge respectively Eq 2320 for E inside a uniform sphere of charge Note When you use Gauss law you should justify in words all the assumptions that you make about your calculation of the electric ux through the Gaussian surface that you choose PHYS 241 Notes for Test 3 Chapter 26 Current and Resistance Review and Summary is on p 698 Know the de nition of electric current Eq 261 and the units of current amperes l ampere l Cs Know the de nition of current density J Given the current density J know how to nd the current 139 using Eq 264 Note that electric current is just the ux of the current density Know the de nition of the resistance R of a conductor Eq 268 and the units of R ohms 1 ohm l voltampere Know Eqs 2610 and 2612 the de nitions of resistivity p and conductivity 6 Units of p Q m Know how to nd the resistance of a wire or cylinder of length L uniform crosssectional area A and uniform resistivity p using Eq 2616 R pLA You should know the formula for the area of a circle of radius r You should know how the resistivity of a material changes with temperature Eq 2617 and that at is called the temperature coef cient of resistivity units lCquot You should know Ohm39s law either as stated in the Review and Summary on p 698 of your text or as stated in the lab You should know Eq 2626 for the rate of energy transfer in an electrical device across which a potential difference Vin volts is maintained P 139 V where 139 is the current in the device in amperes Units of P watts You should know Eqs 2627 and 2628 for the power dissipated by a resistor P z39zR P VzR You should know that this power is dissipated as heat Continued on the other side Chapter 27 Circuits Review and Summary is on p 724 Know the following de nitions Circuit A conducting path around which electric current can ow Seat of electromotive force seat of emf A source of electric energy Electromotive force emf The energy per unit charge converted from nonelectrical form to electrical form in a seat of emf You should know that a seat of emf is a device that does work on charges to maintain a potential difference between its output terminals If dW is the work the device does to force positive charge dq from the negative terminal to the positive terminal then the emf of the device can be calculated as dW 3 7 27 1 dq Know Kirchhoff39s rules and how to use them to find currents in a circuit Know how to find the potential difference between two points in a circuit You may need to use the formula for capacitance C g from Chapter 25 Know that the rate at which chemical energy changes in a battery is P em jg 2717 You may need to use P iZR or P iV from Chapter 26 for the power dissipated by a resistor Know how to derive Equations 277 and 2724 for the equivalent resistance of resistors connected in series and parallel respectively Resistors connected in parallel Voltage across each is the same Resistors connected in series Current through each is the same RC Circuits Know how to derive Equation 2733 for the charge on a charging capacitor and how to derive Equation 2734 for the current in the resistor of an RC circuit with a charging capacitor Know how to derive Equation 2739 for the charge on a discharging capacitor and how to derive Equation 2740 for the current in the resistor of an RC circuit with a discharging capacitor Know how to sketch graphs of Equations 2733 2734 2739 and 2740 Know the formula for the time constant 1 and how it relates to an RC circuit with a charging capacitor and an RC circuit with a discharging capacitor

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