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PHYS 222 Worksheet 5 – Electric Potential Supplemental Instruction Iowa State University Leader: Course: Instructor: Date: Alek Jerauld PHYS 222 Dr. Paula Herrera-Siklódy 1/24/12 Useful Equations Wab (Ub U a ) qq U k 0 r q U kq0 i i ri U q V k q0 r q V k i i ri dq V k r Work done by a conservative force Electric potential energy by two point charges q and q0 Potential energy of charge q0 due to the collection of charges qi Potential due to a point charge. Units: [ 1 V = 1 volt = 1 J/C] Potential due to a collection of point charges Potential due to a continuous distribution of charge b Vb Va E dl Potential difference as an integral of E E V E in terms of V. E is the gradient of V. a Diagrams Related Problems 1) A point charge q1 = +2.40 µC is held stationary at the origin. A second point charge q2 = -4.30 µC moves from the point x = 0.150 m, y = 0 to the point x = 0.250 m, y = 0.250 m. How much work is done by the electric force on q2? W (U b U a ) Ua Ub kq1q2 9(109 )(2.4)(106 )( 4.3)(106 ) 0.6192 J x1 0.150 kq1q2 x2 2 y2 2 9(109 )(2.4)(106 )( 4.3)(106 ) 0.252 0.252 0.2627 J W (U b U a ) ((0.2627) (0.6192)) 0.3565 J 2) Two stationary point charges +3.00 nC and +2.00 nC are separated by a distance of 50.0 cm. An electron is released from rest at a point midway between the two charges and moves along the line connecting the two charges. What is the speed of the electron when it is 10.0 cm from the +3.00-nC charge? KEi U i KE f U f KE f U i U f q q 3(109 ) 2(109 ) 17 U i kqe 1 2 9(109 )(1.6)(1019 ) 2.88(10 ) J r r 0.25 0.25 1i 2i q q U f kqe 1 2 5.04(1017 ) J r1 f r2 f KE mv / 2 U i U f v 2 2(U i U f ) m 2(2.304(1017 ) (3.6(1017 ))) 6.89(106 ) m / s 31 9.11(10 ) 3) A uniform electric field has magnitude E and is directed in the negative x direction. The potential difference between point a (at x = 0.70 m) and point b (at x = 0.85 m) is 370 V. (a) Which point is at a higher potential? a or b E field points towards the direction of lower potential, thus potential at point a is lower that at point b. (b) Calculate the value of E xb Vb Va E dl E ( xb xa ) E xa V 2467 N / C pointing in the negative x xb xa (c) A negative point charge q = -0.200 µC is moved from b to a. Calculate the work done on the point charge by the electric field W q0 V q(Va Vb ) (0.2)(106 )(370) 7.4(105 ) J 4) How much excess charge must be placed on a copper sphere 25.0 cm in diameter so that the potential of its center, relative to infinity, is 1.50 kV? What is the potential of the sphere's surface relative to infinity? E q 4 l 2 0 r d /2 V E dl q q 1 1 dl ( ) 2 4 l 0 4 0 d / 2 q V 4 0 d / 2 1.5(103 )4 (8.85)(10 12 )(0.25 / 2) 20.8 nC V on the surface equals 1.5 kV 5) A very long insulating cylinder of charge of radius 2.60 cm carries a uniform linear density of 16.0 nC/m. If you put one probe of a voltmeter at the surface, how far from the surface must the other probe be placed so that the voltmeter reads 180 V? E 2 l 0 d r r V E dl d r d re r V 2 0 dl (ln(d r ) ln(r )) 2 l 0 2 0 (180)2 8.85(1012 ) r (0.026)e 16(109 ) 0.026 2.26 cm