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*LECTURE Topic 4 POTENTIAL September 19, 2005 Alternate Lecture Titles Back to Physics 2048 ...*

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Slide 2 LECTURE Topic 4 POTENTIAL September 19, 2005 Slide 3 Alternate Lecture Titles Back to Physics 2048 You can run but you cant hide! Slide 4 The PHY 2048 Brain Partition h m A B To move the mass m from the ground to a point a distance h above the ground requires that work be done on the particle. W is the work done by an external force. mgh represents this amount of work and is the POTENTIAL ENERGY of the mass at position h above the ground. The reference level, in this case, was chosen as the ground but since we only deal with differences between Potential Energy Values, we could have chosen another reference. Reference 0 Slide 5 Lets Recall Some more PHY2048 h m A B A mass is dropped from a height h above the ground. What is its velocity when it strikes the ground? We use conservation of energy to compute the answer. Result is independent of the mass m. Slide 6 Using a different reference. y=h m A B y y=b ( reference level) y=0 Still falls to here. Slide 7 Energy Methods Often easier to apply than to solve directly Newtons law equations. Only works for conservative forces. One has to be careful with SIGNS. VERY CAREFUL ! Slide 8 I need some help. Slide 9 THINK ABOUT THIS!!! When an object is moved from one point to another in an Electric Field, It takes energy (work) to move it. This work can be done by an external force (you). FIELD You can also think of this as the FIELD doing the negative of this amount of work on the particle. Slide 10 Lets look at it: move a mass from y i to y f yfyiyfyi External Field Change in potential energy due to external force: Negative of the work done BY THE FIELD. Keep it! Slide 11 Move It! Move the charge at constant velocity so it is in mechanical equilibrium all the time. Ignore the acceleration at the beginning because you have to do the same amount of negative work to stop it when you get there. Slide 12 And also remember: The net work done by a conservative (field) force on a particle moving around a closed path is ZERO! Slide 13 A nice landscape mg h Work done by external force = mgh How much work here by gravitational field? Slide 14 The gravitational case: Slide 15 Someone elses path Slide 16 IMPORTANT The work necessary for an external agent to move a charge from an initial point to a final point is INDEPENDENT OF THE PATH CHOSEN! Slide 17 The Electric Field Is a conservative field. No frictional losses, etc. Is created by charges. When one (external agent) moves a test charge from one point in a field to another, the external agent must do work. This work is equal to the increase in potential energy of the charge. It is also the NEGATIVE of the work done BY THE FIELD in moving the charge from the same points. Slide 18 A few things to remember A conservative force is NOT a Republican. An External Agent is NOT 007. Slide 19 Electric Potential Energy When an electrostatic force acts between two or more charged particles, we can assign an ELECTRIC POTENTIAL ENERGY U to the system. Slide 20 U=PE Example: NOTATION U=PE A B dd E q F Work done by FIELD is Fd Negative of the work done by the FIELD is -Fd Change in Potential Energy is also Fd. The charge sort-of fell to lower potential energy. HIGH U LOWER U Slide 21 Gravity mg Negative of the work done by the FIELD is mg h = U Bottom Line: Things tend to fall down and lower their potential energy. The change, U f U i is NEGATIVE! Slide 22 Electrons have those *^ negative signs. Electrons sometimes seem to be more difficult to deal with because of their negative charge. They seem to go from low potential energy to high. They DO! They always fall AGAINST the field! Strange little things. But if YOU were negative, you would be a little strange too! Slide 23 An Important Example Designed to Create Confusion or Understanding Your Choice! E e A sad and confused Electron. Initial position Final position d The change in potential energy of the electron is the negative of the work done by the field in moving the electron from the initial position to the final position. FORCE negative charge Force against The direction of E Slide 24 An important point In calculating the change in potential energy, we do not allow the charge to gain any kinetic energy. We do this by holding it back. That is why we do EXTERNAL work. When we just release a charge in an electric field, it WILL gain kinetic energy as you will find out in the problems! Remember the demo! Slide 25 AN IMPORTANT DEFINITION Just as the ELECTRIC FIELD was defined as the FORCE per UNIT CHARGE: We define ELECTRICAL POTENTIAL as the POTENTIAL ENERGY PER UNIT CHARGE: VECTOR SCALAR Slide 26 UNITS OF POTENTIAL Slide 27 Watch those #&@% (-) signs!! The electric potential difference V between two points I and f in the electric field is equal to the energy PER UNIT CHARGE between the points: Where W is the work done BY THE FIELD in moving the charge from One point to the other. Slide 28 BREAK Start September 21 (Winter??) Slide 29 Lets move a charge from one point to another via an external force. The external force does work on the particle. The ELECTRIC FIELD also does work on the particle. We move the particle from point i to point f. The change in kinetic energy is equal to the work done by the applied forces. Slide 30 Furthermore If we move a particle through a potential difference of V, the work from an external person necessary to do this is q V Slide 31 Example Electric Field = 2 N/C 1 C d= 100 meters Slide 32 One Step More Slide 33 The Equipotential Surface DEFINED BY It takes NO work to move a charged particle between two points at the same potential. The locus of all possible points that require NO WORK to move the charge to is actually a surface. Slide 34 Example: A Set of Equipotenital Surfaces Slide 35 Back To Yesteryear Slide 36 Field Lines and Equipotentials Equipotential Surface Electric Field Slide 37 Components Equipotential Surface Electric Field E normal E parallel xx Work to move a charge a distance x along the equipotential surface Is Q x E parallel X x Slide 38 BUT This an EQUIPOTENTIAL Surface No work is needed since V=0 for such a surface. Consequently E parallel =0 E must be perpendicular to the equipotential surface Slide 39 Therefore E E E V=constant Slide 40 Field Lines are Perpendicular to the Equipotential Lines Slide 41 Equipotential Slide 42 Consider Two Equipotential Surfaces Close together V V+dV ds a b Work to move a charge q from a to b: E Slide 43 Where I probably wont ask about this. Slide 44 Typical Situation Slide 45 Keep in Mind Force and Displacement are VECTORS! Potential is a SCALAR. Slide 46 UNITS 1 VOLT = 1 Joule/Coulomb For the electric field, the units of N/C can be converted to: 1 (N/C) = 1 (N/C) x 1(V/(J/C)) x 1J/(1 NM) Or 1 N/C = 1 V/m So an acceptable unit for the electric field is now Volts/meter. N/C is still correct as well. Slide 47 In Atomic Physics It is sometimes useful to define an energy in eV or electron volts. One eV is the additional energy that an proton charge would get if it were accelerated through a potential difference of one volt. 1 eV = e x 1V = (1.6 x 10 -19 C) x 1(J/C) = 1.6 x 10 -19 Joules. Nothing mysterious. Slide 48 Coulomb Stuff: A NEW REFERENCE Consider a unit charge (+) being brought from infinity to a distance r from a Charge q: q r To move a unit test charge from infinity to the point at a distance r from the charge q, the external force must do an amount of work that we now can calculate. x Slide 49 The math. This thing must be positive anyway. r final