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# Test 1 study guide chapters 17-21 PHYS 112

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This 15 page Study Guide was uploaded by Rachel Hamilton on Monday February 8, 2016. The Study Guide belongs to PHYS 112 at Old Dominion University taught by Wesselman in Spring 2016. Since its upload, it has received 95 views. For similar materials see Physics in Physics 2 at Old Dominion University.

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Date Created: 02/08/16

PHYSICS 112 TEST 1 STUDY GUIDE CHAPTERS 17-21 CHAPTER 17 o Electric Charges Two types Positive Negative Alike charges repel Opposites attract Mass of electron 9.109*10 -31kg Mass of proton -27 1.673*10 kg Mass of neutron 1.675*10 kg7 The net charge of a neutral atom is zero o Conductors and Insulators Conductor Object that allows the transfer/flow of energy o Usually metals Insulator Materials that does not allow the transfer/flow of energy o Non-metals such as rubber Semiconductors Intermediate in properties between good conductors and good insulators Induction Process in which an object can give another object a charge of OPPOSITE sign without losing any of its own When electrons on surface are repelled by excess electrons on an object they shift away. This causes excess negative charges because they are unable to escape. These excess charges are called induced charges. o Conservation and Quantization of Charge The algebraic sum of all the electric charges in any closed system is constant. The transfer of charges from one object to another is the only way to acquire a net charge o Coulomb’s Law States that the magnitude F of the force that each of two point charges q 1nd q a2distance r apart exerts on the other directly proportional to the square of the distance between them The two forces are ALWAYS equal in magnitude and opposite in direction even if the charges are not equal o Due to Newton’s 3 law: where there is one force, another force with the same magnitude acts upon it in opposite direction When the distance is doubled, the force is decreased by ¼ its initial value. Magnitude of charge of election or proton (e) o 1.6*10 C -19 o Electric Field and Electric Charge E=F/q If q is negative, then E and F are opposite If q is positive, then E and F are the same Field lines At every point in space the electric field vector is tangent to the field line at that point Field lines are close together where the magnitude E is large and farther apart when E is small Field lines point away from positive charges and toward negative o Gauss’s Law Gauss’s Law is a relation between the field at all the points on the surface and the total charge enclosed within the surface Electric flux The product of the magnitude E of the electric field and the area A The total electric flux coming out of any closed surface is proportional to the total electric charge inside the surface The flux only depends of the charge The flux is independent of the radius CHAPTER 18 o Electric Potential Energy The work done on an object W=Fscos(theta) or W=Fs From this equation W=Fs we are able to get W=qEs because F=qE Potential Energy: U=mgy For electric potential energy U=qEy Mg is replaced by F which equals qE Work equals the change in potential When y isagreater than y thebparticle moves in the same direction as the E field, U decreases, and the field does positive work When y is less than y the particle moves in the a b opposite direction to E, U increases, and the field does negative work Potential energy of point charges U=k(q q1/2) If q1and q 2ave the same sign the interaction is repulsive, the work is positive, and U is positive at any finite separation If q1and q 2ave opposite signs, the interaction is attractive and U is negative o Potential Potential is the potential energy per unit of charge V=U/q V=k(q/r) May often be referred to as voltage o Equipotential surfaces Surface with different potentials can never touch or intersect The potential energy for a test charge is the same at every point on a given equipotential surface so the E field does no work when it moves from point to point E must be perpendicular to the surface at every point If it were tangent, then it would do work o Capacitors Capacitor is a device that stores electric potential energy and electric charge When charges with equal magnitude and opposite sign are placed on conductors, an electric field is established and there is a potential difference between them. C=Q/V The ratio of the magnitude of the charge Q to the magnitude of the potential difference between the conductors SI Unit: Farad (F) or Coulomb/Volt (C/V) Parallel plate capacitors The field between the plates is uniform and the charges are uniformly distributed o E=Q/e A 0 o e 8.854*10 -12C /N*m 2 0= o V=Ed Series vs Parallel Series o Potential difference is maintained o Capacitors are both initially uncharged o The magnitude of the charge on all of the plates is the same because of the conservation of charge. o The total potential difference across all of the capacitors is the sum of the individual potential differences V=Q/C=Q(1/C+1/C+…) o Equivalent capacitance is the capacitance of a single capacitor for which the charge Q is the same as for the combination when the potential difference V is the same o The reciprocal of the equivalent capacitance of a series combination equals the sum of the reciprocals of the individual capacitances 1/Ceq1/C +1/C +…2 Parallel o The potential difference is the same for both capacitors o The equivalent capacitance equals the sum of the individual capacitances CeqC +1 +…2 o Dielectrics Nonconducting material between capacitor plates Three functions Solves mechanical problem of maintaining two large metal sheets at a very small separation without contact Permits conducting through a material that is supposed to be an insulator due to dielectric breakdown The capacitance of a capacitor of given dimensions is greater when there is a is a dielectric between the plates C=KC 0 K is the dielectric constant of a material When the charge is constant, the potential difference is reduced by a factor K V=V 0K The electric field must decrease by the same factor K if the potential difference does E=E /0 Because E is smaller when the dielectric is present means that the surface charge density is also smaller The charge of the conducting plates does not change, but an induced charge of the opposite sign appears on each surface of the dielectric CHAPTER 19 o Current Any motion of charge rom one region of a conductor to another I=Q/t When moving charges are positive, the current flows with them When moving charges are negative, the current flows against them When there is a steady current, or a closed loop, the total charge in every segment is constant due to conservation of charge The amount of flow out of one end equals the rate of flow in at the other end o Resistance and Ohm’s Law Resistance When the potential difference between the ends of a conductor is proportional to the current in the conductor, the ratio V/I is called the resistance of the conductor o R=V/I Also referred to as Ohm’s Law Resistivity R=p(L/A) p is the resistivity o Emf and Circuits For a conductor to have a steady current, it must be part of a path that forms a complete circuit The path cannot consist entirely of resistors; they decrease the potential energy. There must be part of the circuit where potential energy increases Emf is the energy per unit of charge similar potential Devices with emfs convert energy fo some form into electrical potential energy and transfers it into the circuit where the device is connected The potential difference is equal to the emf When a charge q flows aroung the circuit, the potential rise (emf) as it passes through the source is numerically equal to the potential drop as it passes through the resistor. Once (emf) and R are determined you can then find the current I o The current is the same at every point in the circuit o (emf)=V=IR Internal resistance (r) is constant. The current through r has an associated drop in potential equal to Ir o V=(emf)-Ir Shows that the algebraic sum of the potential differences and emf’s around the closed path is zero The potential V called the terminal voltage is less than the emf because of the term Ir representing the potential drop across the internal resistance r o (emf)-Ir=IR o I=((emf)/R+r) The second equation explains that the current equal the source emf divided by the TOTAL resistance. If the current were different at different points, there would be a continuing accumulation of charge at some points and the current would not be constant o Energy and Power in Electric Circuits The work done on a charge q that passes through the circuit element equals the product q and the potential difference V. W=VQ=VIt This work represents the electrical energy transferred into the circuit. The time rate of energy transfer is power W/t= P=VI If the potential at b is more than at a, then V is negative and there is a net transfer out of the circuit P=VI=I R=V /R2 o Used when calculating the power dissipated through a resistor P=VI=(emf)I-I2r o Represents the net electrical output of the source in which the source delivers electrical energy to the remainder of the circuit. o Resistors in Series and Parallel Series V=IR o V=I(R +R1+…)2 Equivalent resistance for series is opposite of that for capacitors o The resistance is found with the sum of all resistors within a circuit R eq +1 +… 2 o The equivalent resistance is always greater than that of any individual resistance Parallel The potential difference between terminals must be the same and equal V Charge is neither accumulating nor draining out o The total current I must equal the sum of the three currents in the resistors I=V(1/R 11/R +…2 Equivalent resistance is opposite that of parallel capacitors Found using the reciprocal of each resistance o 1/R =eqR +1/1 +… 2 o After entering fractions into calculator, raise answer to the -1 power to determine R eq o Equivalent resistance is always less than any individual resistance o Kirchhoff’s Rules Junction/point Rule Junction is a point where three or more conductors meet o Also called nodes or branch points The algebraic sum of the currents into any junction is zero o I=0 Based on the conservation of electric charge, o No charge can accumulate at a junction The total charge entering the junction equals the amount leaving Loop Rule A loop is any closed conducting path The algebraic sum of the potential differences, or any emf’s, in any loop must equal zero o V(or emf)=0 Based on the conservation of energy o The electrostatic field is a conservative force field o The charges travel around the loop back to their original position which makes the total change zero o Resistance-Capacitance Circuits The overall charge of a capacitor starts off as zero when the switch is opened When the switch is closed the charges accumulate at both ends of the capacitor While the capacitor becomes charged, the current and potential difference decrease When the capacitor reaches its full charge, the current and potential is zero o The charges basically form a blockage The ending current and overall charge can be found using: o I=I e0 -t/RC o q=Q (1-e-t/)C final o Power Distribution The maximum current available is limited by the resistance of the wires CHAPTER 20 o Magnetism Described in terms of poles North pole is the end of the bar magnet that points toward the earth’s geographic north pole South pole is just the other end Opposite poles attract Alike poles repel When you cut a magnet in half does not provide two separate north and south poles, each half creates its own North and South pole Geographic south pole is actually magnetic north pole o Compasses can be set to either the geographic north pole, or true north Electromagnets produce magnetic effects caused by an electric current o Magnetic Field and Magnetic Force A few key concepts: A permanent magnet, a moving charge, or a current creates a magnetic field at all points in the surrounding space The magnetic fields exert a force F on any other moving charge or current that is present in the field The magnetic field is a vector field, just like an electric field represented by the symbol B Field lines represent the magnetic field Lines are tangent to B Draw the number of lines per unit area perpendicular to the lines at a give point to be proportional to the magnitude of the field For a bar magnet the field lines point from the N to S They do not point in the direction of the force on a charge Magnetic force The magnitude of the force is proportional to the magnitude of the field o If you double the magnitude of the field without changing the charge or its velocity, the magnitude of the force doubles The magnetic force is also proportional to the particle’s speed o A charged particle at rest has no magnetic force o The force F does not have the same direction as magnetic field B The force is always perpendicular to both B and its velocity v F=qvB=qvBsin o Right hand rule (for positive charges) Curl fingers in direction of v, your thumb should be perpendicular of field B. The direction of your thumb is the force F (for negative charges) do the same thing then reverse the direction of the force o Motion of Charged Particles in a Magnetic Field Motion of particle along a magnetic field is determined by Newton’s Law The force is always perpendicular to v so it cannot change the magnitude of the velocity, only its direction 2 o F=qvB=m(v /R) For a given charge, a larger magnetic field increases the force and pulls the particle into a smaller radius If the charge q is negative, the particle moves clockwise around the orbit o Magnetic Force on a Current-Carrying Capacitor The force is always perpendicular to both the conductor and the field, with the direction determined by the right hand rule F=IlB=IlBsin When moving charges are negative, then an upward current corresponds to a downward drift velocity o Force and torque on a Current Loop The torque tends to rotate the loop in the direction of decreasing , which is toward the stable equilibrium position and the loop lies in the x-y plane perpendicular to the direction of the field B =IABsin For solenoids (winding of wire) o The torque equals the sum of the torques on the individual turns (N) =NIABsin o Torque tends to rotate solenoid’s axis is parallel to the field Makes torque equal zero o Magnetic Field of Conductor The magnetic field produced by long, straight conductor carrying a current I at a distance r from the axis of the conductor has magnitude B B= I/2r 0 -7 = 4*10 T*m/A o the permeability of vacuum o Current Loops Magnetic field at center of loop B= I02R If a coil of N loops are closely spaced and all have the same radius, then each loop contributes equally to the field o B= NI02R At points along axis of loop, the B field is parallel to the axis o Its magnitude is greatest at center of loop and decreases on both sides Solenoid o A helical winding of wire o All turns carry the same current I o The total B field at every point is the vector sum of individual turns o Field is found to be most intense in the center and less intense near the ends o The magnetic field depends on the number of terms per unit length of the solenoid B= nI 0 o Magnetic Field Calculations Law of Bivot and Savart The magnitude of B due to a segment of conductor with length l, carrying2a current I: o B=( /0)Ilsin/r o B is not along the line form the source point At each point It is perpendicular to the plane containing this line and direction of the segment l o Magnetic materials Paramagnetic Orientation with an external field Diamagnetism Orientation against an external field Ferromagnetism Strong interactions between microscopic current loops to line up parallel to each other in magnetic domains When there is no applied field, the orientations of the domain magnetizations are random and net magnetization is zero As the external field increases, a point is reached where all current loops’ axis are parallel to the field o Called saturation magnetization CHAPTER 21 o Magnetic Flux The total flux through the surface is the sum of the contributions from the individual area elements =BAcos When B is perpendicular to A, =BA When B is at an angle to the perpendicular A, =BAcos When B is parallel to A at 90, =0 o Faraday’s Law States that the induced emf in a circuit is directly proportional to the time rate of change of the magnetic flux through the circuit EMF=/t o If there is a coil with N turns, then… EMF=N(/t) o Lenz’s Law States that the direction of any magnetically induced current or emf is such to oppose the direction of the phenomenon causing it When the flux through the loop is increasing, the induced magnetic field points opposite to the original field When the flux through the loop is decreasing, the induced magnetic field points in the same direction as the original field o Self-inductance Represented by L Is the magnitude of the self-induced emf per unit rate of change of current EMF=L(i/t) You can find the direction of the self-induced emf from Lenz’s law The induced emf must oppose the increasing current o Transformers Consists of two coils Winding in which power is applied is called primary Winding in which power is delivered is secondary Flux is the same within both coils o R-L Circuits The voltage across a resistor depends on the current V=IR The voltage across a inductor depends on the rate of change of the current (i/t) V=L(i/t) o L-C Circuits As the capacitor discharges, the rate of change of the current decreases After time, the current and magnetic field equal zero and the potential difference and the charge are OPPOSITE of what it began with and then return to their original after time Think of it like oscillations on a sin wave o You start with both potential and charge above zero, by the end of the wavelength they are both zero, and then after time make their way back above zero, and so on To find the angular frequency: =(1/LC) QUESTIONS 1. A spherical balloon contains a charge +Q uniformly distributed over its surface. When it has a diameter D, the electric field at its surface has magnitude E. If the balloon is now blown up to twice this diameter without changing the charge, the electric field at its surface is: a. 4E b. 2E c. E d. E/2 e. E/4 2. A charge +Q is suspended by a silk thread inside of a neutral metal box without touching the metal. What is true about the charge on the inner and outer surfaces of the box? a. The charge on both the inner and the outer surfaces is zero b. The charge is –Q on the inner surface and +Q on the outer surface c. The charge is +Q on the inner surface and –Q on the outer surface d. The charge on both the inner and outer surface is +Q 3. A parallel-plate capacitor having circular plates of radius R and separation d is held at a fixed potential difference by a battery. If the plates are moved closer together while they are held at the same potential difference… a. The amount of charge on each of them will increase b. The amount of charge on each of them will decrease c. The amount of charge on each of them will stay the same d. The energy stored in the capacitor increases 4. When a certain capacitor carries charge of magnitude Q on each of its plates, it stores energy U. In order to store twice as much energy how much charge should it have on its plates? a. 2Q b. 2Q c. 4Q d. 8Q 5. A cylindrical metal rod has a resistance R. If both its length and its diameter are tipled, its new resistance will be: a. R b. 9R c. R/3 d. 3R 6. Two identical metal rods are welded together end to end. If each rod has a length L and resistivity p, the resistivity of the combination will be: a. 4p b. 2p c. p d. p/2 7. Three identical light bulbs, A, B, and C, are connected in the circuit shown. When the switch S is closed… a. The brightness of A and B remains the same as it was, but C goes out b. The brightness of A and B remains the same as it was, but C will be about half as bright c. The brightness of A and B decreases, and C goes out d. The brightness of A and B increases, and C will be about half as bright as it was e. The brightness of A and B increase, but C goes out 8. An electron traveling at high speed enters a uniform magnetic field directed perpendicular to its path. Which of the following quantities will change while the electron travels through the field? a. Speed b. Velocity c. Acceleration d. Kinetic energy e. Potential energy 9. A solenoid is connected to a battery in the figure shown, and a bar magnet is placed near by. What is the direction of the magnetic force that this solenoid exerts on the bar magnet? a. Upward b. Downward c. To the right, away from the solenoid d. To the left, toward the solenoid 10. A steady current of 1.5 A flows through the solenoid shown in the figure below. The current induced in the loop, as viewed from the right, is directed a. Clockwise b. Counterclockwise c. Zero 11. If the electrical potential energy of two point charges is U when they are distance d apart, their potential energy when they are twice as far apart will be a. U/4 b. U/2 c. 2U d. 4U 12. An electron is moving horizontally in a laboratory when a uniform electric field is suddenly turned on. This field points vertically downward. Which of the paths shown will the electron follow, assuming gravity can be neglected? 13. Three equal point charges are held in place as shown in figure. If F1is the force on q due to Q 1 and F 2s the force on q due to Q , 2ow do F and1 F compare? 2 a. F 12F 2 b. F 13F 2 c. F 14F 2 d. F 19F 2 14. The electric potential due to a single point charge Q is +400V at a point that is 0.90m to the right of Q. The electric potential at a point 0.90m to the left of Q is a. -400V b. +200V c. +400V 15. The two coils shown in the figure are parallel to each other and are connected to batteries. Coil A is held in place, but coil C is free to move. After the switch S is closed, coil C will initially move a. Toward coil A b. Away from coil A c. Upward d. Downward

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