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Score: /100 Physics 212 - Spring 2000 Recitation Activity 5: Electric Potential Solution INSTRUCTOR: Redwing DATE: January 25, 2000 NAME: This activity is based on the following concepts: The ELECTRIC POTENTIAL ENERGY of a point charge is equal to the work done by the electric field on the point charge as the charge moves from infinity to its final position. U = -Winfinity. The ELECTRIC POTENTIAL V at a point is the ELECTRIC POTENTIAL ENERGY per unit charge at that point. V = U / q Potential due to point charge: V 1 q 4 0 r Potential due to an electric dipole: V 1 p cos , p = qd. 4 0 r2 dq . Potential due to a continuous charge distribution: V 1 40 r The ELECTRIC POTENTIAL DIFFERENCE, V, is the difference in ELECTRIC POTENTIAL between two points. V = Vf – Vi. f The potential difference between any points can be found using the electric field: V f Vi E.ds i Electric field can be calculated from the electric potential: E V . s s All points on an EQUIPOTENTIAL SURFACE all have the same potential: Work done on a test charge in moving it from one surface to another is independent of the path chosen or the locations of the initial and final points on these surfaces. 3 Electric field is always perpendicular to these surfaces. B + + A Q1. The figure shows three paths along which we can move 2 positively charged sphere A closer to positively charged sphere B, which is fixed in place. 1 (a) Would sphere A be moved to a higher or lower electric potential? (b) Is the work done by our force to move the sphere positive, negative or zero? (c) Is the work done by the electric field (due to the second sphere) positive, negative or zero? (d) Rank the paths according to the work our force to move does, greatest first. all same Q2. The figure shows four arrangements of charged particles, all the same distance from the origin. Rank the situations according to the net electric potential at the origin, most positive first. Take the potential to be zero at infinity. b; then a, c, d all tie +2q -2q -3q -2q -2q +2q -9q -q -2q (a) -4q (b) +2q -7q (c) (d) Q3. An electron is moved from infinity to the midpoint between two charged particles fixed in place. Is the work done on the incoming electron by the electric field positive, negative, or zero? e e e e e p (a) (b) In (a) the work done by the electric field is positive, negative, or zero. (circle one) In (b) the work done by the electric field is positive, negative, or zero. (circle one) Q4. The electric potential varies along the xaxis as shown in the following graph. For each interval ab, bc, cd, de, ef, fg and gh, determine the x component of the electric field. (Ignore behavior at the interval end points.) V Ex x 12V E xab 6V E xbc 0V m m 2m 6V E xcd 3V m 2m 6V E xde 3V m 2m 8V E xef 8V E xfg 0V m m 1m 8V E xgh 4V m 2m Q5. Using the data from Q4, plot Ex versus x. (Properly label your plot.) Scoring Guidelines: 100 90 75 60 40 0 All correct miss one some correct none to few correct, but shows effort Turned in paper, but no real effort No paper 14 b c V (V) 10 d 6 2 a -8 -3 h e -2 x (m) 2 7 -6 f -10 g -14 8 E(V/m) 4 x(m) 0 -8 -4 0 -4 -8 4 8