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PHYS 222 SI Exam Review 3/31/2013 Answer: D Answer: D,D Answer: D,C What to do to prepare β’ Review all clicker questions, but more importantly know WHY β’ Review quizzes β’ Make sure you know what all the equations do, and when to use them SI Leader Secrets! Extra problems? Visit the website below to get past exams all the way back to 2001!! (Note: the link below has stuff that you wouldnβt otherwise see) http://course.physastro.iastate.edu/phys222/ex ams/ExamArchive222/exams/ π π‘ =π β 1β π π‘ =π 0 π = π πΆ I π‘ =πΌ 0 π‘ β π π π‘ β π π π‘ β π π β’ These are all equations used for an RC circuit. π π‘ =π β 1β I π‘ =πΌ 0 π‘ β π π, π‘ β π π π πΌ 0 = π β’ Used to find the charge Q on the capacitor in an RC circuit that initially has no charge and is slowly brought to a maximum charge π β . β’ What is π? π = π πΆ β’ π β = πΆπ π π‘ I π‘ π‘ β = π 0 π π, π π‘ β = πΌ 0 π π, 0 = πΆπ β’ Used to find the charge Q on the capacitor in an RC circuit that initially has charge Q(0) and has been disconnected from the power source. β’ I(t) is used to find the current in the resulting circuit. As before, π = π πΆ π = π(π¬ + π × π©) β’ Used to find the force on a point charge of charge q in an electric field E and magnetic field B. β’ Notice that the magnetic force is π × π©, and only exists if the charge is moving. ππ = πΌπ π × π© β’ This is the differential form of the magnetic force on a length of wire carrying current. β’ Probably more useful in this form: β π = πΌπ³ × π© β’ Note that if the wire and B field are pointing in the same direction, the force is zero. Ξ¦π΅ = β« π© β π π¨ Ξ¦π΅ is the magnetic flux through a closed surface. Ex: A uniform B field of 5 T goes through a circular loop of wire of radius 10 m, What is the magnetic flux? Ans: Ξ¦π΅ = 5 β π β 102 = 500π T β m2 ππ£ π = ππ΅ β’ Here, a charge of magnitude q and mass m is acted on by a constant B field. As a result, the charge moves in a circle of radius R and its tangential speed is v. π = πΌπ¨ β’ This is the equation for the magnetic dipole (π) of a loop of current. β’ π is a vector β’ As an example, if the radius is 4 m and I=2, then π = ππ up π=π×π© β’ This gives the torque on a magnetic dipole by a magnetic field. β’ Note that torque is zero if the magnetic dipole and the B field point in the same direction. π = βπ β π© β’ This gives the potential energy of a magnetic dipole in a magnetic field. π0 ππ × π π©= 4π π 2 β’ The equation for the magnetic field produced by a moving charge q at a speed v. β’ π is just the distance away from the moving charge. β’ π × π just means to use the right hand rule to determine which direction the magnetic field points. π0 πΌπ π × π π π© = 4π π 2 β’ Same equation as before, except that instead of a single point charge moving, we have a current I. β’ This equation is probably easier to use in its linear, non-differential form π© = π0 πΌπ³×π , 2 4π π β’ ππ₯ × π just means to use the right hand rule to determine which direction the magnetic field points. Right-hand rule π0 πΌ π©= 2πr β’ This is the magnetic field a distance r away from an infinite straight wire carrying current I. β’ The direction of the field is given by the right hand rule. πΉ π0 πΌπΌ β² = πΏ 2ππ β’ This gives the force between two parallel wires. One wire carries current I, the other wire carries current Iβ. β’ If the currents are pointing in the same direction, the force is attractive. If they are opposite, the force is repulsive. β’ Is the force attractive or repulsive? β’ Answer: attractive. 1 2 π = π 0 π0 β’ I doubt youβd find a practical use for this equation in exam 2, because it really only says that the speed of light squared is equal to the inverse of the products of two constants. Cool, but not really something testable. π0 π΅π₯ = 2 2 π₯ 2 ππΌπ + 3 2 π 2 β’ Letβs say you have a wire bent in a circle of radius a (in the picture itβs shown as R), with N turns. This equation gives the B field at the center of the circle a distance x above the center (if the circle is in the x-y plane, the variable x is the z coordinate). β’ The direction of the B field is given by the right hand rule, as discussed earlier. π0 ππΌ π΅π₯ = 2π β’ This equation is really just a special case of the previous one. This is the B field at the center of the circle, in the plane. Question: β’ In the picture does the B field produced by the current point into the page or out of the page? Question: β’ In the picture does the B field produced by the current point into the page or out of the page? β’ Answer: Into the page. π΅ = π0 ππΌ β’ This is the equation for the field inside of a solenoid. β’ Note that it is a uniform field (i.e. everywhere inside of the solenoid itβs the same). β’ Lowercase n is the turns per length. π© β π π = π0 πΌπππ β’ This is sometimes known as Ampereβs law. β’ Can be used to derive many magnetic fields, π0 πΌ for example this one: π© = . (Field away 2πr from any infinite straight wire) πΞ¦π΅ π = βπ ππ‘ β’ This equation is known by many names, including Faradayβs Law and Lenzβs Law, depending on who you talk to. β’ Basically it says that a current loop without a voltage or current source can have an induced voltage if thereβs a changing magnetic flux inside the loop. β’ Note that the direction of the EMF is OPPOSITE the change in flux. π= π × π© β π π β’ This is just another way of expressing the EMF. β’ Recall q(π × π©) is the magnetic force, so here weβre sort of (thereβs no q up there) saying that the path integral of the magnetic force is equal to the emf. πΞ¦π΅ π¬ β π π = β ππ‘ β’ This just says that an induced E field is what causes the induced EMF seen in the earlier πΞ¦π΅ equation: π = βπ ππ‘ β’ Notice how thereβs an N missing in the equation up top. Thatβs because Ξ¦B includes the N already, whereas in the bottom equation it doesnβt. π© β π π = π0 ππΆ + ππ· πππ β’ This is a copy of an equation we saw earlier, except that it includes the displacement current. β’ What is the displacement current? The equation is on the next page, but the physical meaning is that itβs not a true current, but rather a mathematical construction to deal with changes in electric flux. πΞ¦πΈ ππ· = π ππ‘ β’ Hereβs the equation for displacement current. ππππ π¬ β π π¨ = π0 β’ One of the so-called βMaxwellβs Equationsβ β’ Also known as Gaussβs law. β’ Used to calculate the E fields for many common charge shapes, such as spheres and cylinders. (Theoretically can be used for complicated ones too, but that requires fancy mathematical software) π© β π π¨ = 0 β’ One of the so-called βMaxwellβs Equationsβ β’ Says that the magnetic flux through a closed, 3-D surface is always zero. πΞ¦π΅ π¬ β π π = β ππ‘ β’ One of the so-called βMaxwellβs Equationsβ β’ This is basically the same as the induced EMF equation. π© β π π = π0 πΞ¦πΈ π πΆ + π0 ππ‘ ππππ β’ One of the so-called βMaxwellβs Equationsβ β’ This equation basically appears twice on the equation sheet. ππ2 π1 = βπ ππ‘ β’ If you have two loops of current with mutual inductance M, and a current i2 is going through one of them, then an emf π1 (voltage) is produced through the other one, which excites a current in that one. ππ1 π2 = βπ ππ‘ β’ If you have two loops of current with mutual inductance M, and a current i1 is going through one of them, then an emf π2 (voltage) is produced through the other one, which excites a current in that one. β’ Basically the same idea as the last equation. π1 Ξ¦π΅2 π2 Ξ¦π΅2 π= = π1 π1 β’ The definition of mutual inductance M. Use the side of the equation that is relevant. β’ Note that although it appears that M depends on current i, the fact of the matter is that M never depends on i because the i in the numerator cancels with the i in the denominator. β’ There is an i in the numerator because flux depends on B, and B depends on i. ππ π = βπΏ ππ‘ β’ This is the induced emf across an inductor. Note that the induced emf occurs opposite the change in current. πΞ¦π΅ πΏ= π β’ Definition of self-inductance L. π = πΌβ (1 β π‘ β π π) β’ Current across an inductor in an LR circuit when you just start flowing current in the circuit. π= π‘ β πΌ0 π π β’ Current across an inductor in an LR circuit when you just stop flowing current in the circuit. πΏ π= π β’ The time constant in LR circuits. 2 πΏ = π0 π πΏπ΄ β’ Self inductance of a solenoid of n turns per length, of length L, and cross sectional area A. 1 2 π = πΏπΌ 2 β’ Energy contained within an inductor (i.e. solenoid). 2 π΅ π’= 2π0 β’ Energy density for a point with a magnetic field B. β’ Not really covered in lecture as far as I recall π = π0 cos(ππ‘ + π) π= 1 πΏπΆ β’ The equation that tells you the charge q on a capacitor in an LC circuit. β’ Notice that itβs oscillatory- Simple Harmonic Motion! β’ The frequency π depends on L and C π= π β π‘ π0 π 2πΏ β² π = β² cos(π π‘ + π) 1 β( πΏπΆ β π 2 ) 2 4πΏ β’ This is an RLC circuit. β’ The idea is similar to the LC circuit, except that now the charge q is also exponentially decreasing as it oscillates. β’ The oscillation frequency depends on L, C, and R. Past exam problemsβ¦. Answer: C Answer: A Answer: D Answer: B Answers: D, B Answers: A,D Answer: D Answer: B, D Answer: D Answers: C, B Answers: C, B Answers: E, B Answers: A,D Answer: E C, D, E D, B D, D D