A 12-V battery does 1200 J of work transferring charge. How much charge is transferred? A source of 1.0 µc is meters is from a positive test

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1 1 A source of 1.0 µc is meters is from a positive test charge of 2.0 µc. (a) What is the force on the test charge? (b) What is the potential energy of the test charge? (c) What is the strength of the field intensity at this distance? (d) What is the field potential at this distance? 6 A 12-V battery does 1200 J of work transferring charge. How much charge is transferred? 1.0 x 10 2 C (a) 20 N (b).61 J (c) 1.0 x 10 7 N/C (d) 3 x 10 5 J/C 7 It takes 8.00 mj to move a charge of 4.00 mc from point A to point C in an electric field. What is the potential difference between the two points? 2 A positive charge of 8.0 x 10-4 C is separated by.30 m from a source charge of -2.0 x 10-4 C (a) What is the force on the test charge? (b) What is the potential energy possessed by the test charge. (c) What is the field strength of the source? (d) What is the field potential x 10 3 V A spark will jump between two people if the electric field exceeds 4.0 x 10 6 V/m. You shuffle across a rug and a spark jumps when you put your finger 0.15 cm from another person's arm. Calculate the potential difference between your body and the other person's arm. 3 (a) x 10 4 N (b) 4.76 x 10 3 J (c) 1.98 x 10 7 N/C (d) 5.96 x 10 6 J/C What potential difference is applied to two metal plates m apart if the electric field between them is 2.50 x 10 3 N/C? x 10 3 V A proton gains 9.6 x J of electric PE while being moved from x to y. (a) What is the potential difference between x and y. (b) Which point is the higher potential? 1.25 x 10 3 V (a) 6 x 10 7 V (b) point Y 4 What is the unit of potential difference in terms of m, kg, s, and C? V= J/C or N.m/C or ((kg.m)/(s 2.m))/C or (kg.m 2 )/(s 2 C) 10 The difference of potential between the terminals of a battery is 6 V (a) How much work is done when a series of negative charges totaling 0.5 C are moved from one terminal to another? (b) How many elementary charges are involved? (a) 3 joules (b) 3.12 x electrons 5 An electron is moved through a potential difference of 500 V. How much work is done on the electron? x 10-17

2 11 A proton is accelerated over a difference of potential of 50,000 V. (a) How much work in electron volts is done on the proton? Remember an electron volt is a unit of energy. The amount of energy necessary to move an electron across a potential of 1 Volt (1.6 x J) (b) Express this in joules. 15 Draw in a few equipotential lines in shown in the figure. 12 (a) 50,000 ev (b) 8.0 x J Two points are at the same potential. (a) Does this mean that no work is done in moving a test charge from one point to the other? (b) Does this imply that no force need be exerted? Explain. 16 The work done by an external force to move a 8.50 μc charge from point a to point b is 15.0 x 10-4 J. If the charge was started from rest and had 4.82 x 10-4 J of kinetic energy when it reached point b, what must be the potential difference between a and b? 13 (a) no net work (b) no force (a) If a negative charge is initially at rest in an electric field, will it move toward a region of higher potential or lower potential? (b) What about a positive charge? (c) How does the potential energy of the charge change in each instance? x 10 2 V (a) What is the speed of an electron with kinetic energy of 750 ev? (b) What is the speed of an electron with kinetic energy of 3.2 kev? 1.6 x 10 7 m/s 3.4 x 10 7 m/s (a) Negative charge move toward higher potential (b) Positive charge will move toward lower potential (c) Potential energy of each will decrease. 18 A +35 μc point charge is placed 32 cm from an identical +35 μc charge. How much work would be required to move a μc test charge from a point midway between them to a point 12 cm closer to either of the charges? 14 (a) State clearly the difference between electric potential and electric field, (b) State clearly the difference between electric potential and electric potential energy. 2.5 J (a) Electric Potential is scalar Electric Field is Vector (b) Electric potential energy is work against the electric force. 19 (a) What is the electric potential a distance of 2.5 x m away from a proton? (b) What is the electric potential energy of a system that consists of two protons 2.5 x m apart as might occur inside a typical nucleus? (a) 5.8 x 10 5 V (b) 9.2 x J

3 20 Three point charges are arranged at the corners of a square of side L as shown in the figure. What is the potential at the fourth corner (point A), taking V = 0 at a great distance? 24 Consider point a which is 72 cm north of a 3.8 μc point charge, and point b which is 88 cm west of the charge as shown in the figure. (a) Determine V ba = V b V a. (b) Determine E ba = E b E a (magnitude and direction). 21 Two identical +9.5 μc point charges are initially 3.5 cm from each other. If they are released at the same instant from rest, how fast will each be moving when they are very far away from each other? Assume they have identical masses of 1.0 mg. 4.8 x10 3 m/s 25 (a) 8.6 x 10 3 V (b) 7.9 x 10 4 V/m 56 0 How much voltage must be used to accelerate a proton (radius about 1.2 x m) so that it has sufficient energy to just penetrate a silicon nucleus? A silicon nucleus has a charge of +14e, and its radius is about 3.6 x m. Assume the potential is that for point charges. 22 Two point charges, 3.0 μc and 2.0 μc, are placed 5.0 cm apart on the x axis. (Let V = 0 at r = ). (a) At what points along the x axis is the electric field zero? (b) At what points along the x axis is the potential zero? (a) 22 cm left of q 2 (b) 2.0 cm from the negative charge towards the positive charge, and 10 cm from the negative charge away from the positive charge x 10 6 V In the Bohr model of the hydrogen atom, an electron orbits a proton (the nucleus) in a circular orbit of radius 0.53 x m (a) What is the electric potential at the electron s orbit due to the proton? (b) What is the kinetic energy of the electron? (c) What is the total energy of the electron in its orbit? (d) What is the ioni zation energy that is, the energy required to remove the electron from the atom and take it to r =, at rest? Express the results of parts b, c, and d in joules and ev. 23 How much work must be done to bring three electrons from a great distance apart to 1.0 x m from one another (at the corners of an equilateral triangle)? 6.9 x J (a) 27 V (b) 2.2 x J 14 ev (c) -2.2 x J -14 ev (d) 2.2 x J 14 ev

4 27 In a given CRT, electrons are accelerated horizontally by 7.0 kv. They then pass through a uniform electric field E for a distance of 2.8 cm, which deflects them upward so they reach the screen top 22 cm away, 11 cm above the center. Estimate the value of E. 31 A +33 μc point charge is placed 36 cm from an identical +33 μc charge. A 1.5 μc charge is moved from point a to point b in the figure. What is the change in potential energy? 2.9 x10 5 V/m 28 Electrons are accelerated by 6.0 kv in a CRT. The screen is 30 cm wide and is 34 cm from the 2.6-cm-long deflection plates. Over what range must the horizontally deflecting electric field vary to sweep the beam fully across the screen? 1.5 J x 10 5 V/m to x 10 5 V/m 32 A uniform electric field of magnitude 325 V/m is directed in the negative y direction in the figure. The coordinates of point A are ( 0.200, 0.300) m, and those of point B are (0.400, 0.500) m. Calculate the potential difference V B - V A, using the blue path. 29 In a television picture tube, electrons are accelerated by thousands of volts through a vacuum. If a television set were laid on its back, would electrons be able to move upward against the force of gravity? What potential difference, acting over a distance of 3.0 cm, would be needed to balance the downward force of gravity so that an electron would remain stationary? Assume that the electric field is uniform. 1.7 x V 30 Near the surface of the Earth there is an electric field of about 150 V/m which points downward. Two identical balls with mass m = kg are dropped from a height of 2.00 m, but one of the balls is positively charged with q 1 = 650 μc, and the second is negatively charged with q 2 = 650 μc. Use conservation of energy to determine the difference in the speed of the two balls when they hit the ground. (Neglect air resistance.) V On planet Tehar, the free-fall acceleration is the same as that on Earth but there is also a strong downward electric field that is uniform close to the planet s surface. A 2.00-kg ball having a charge of 5.00 µc is thrown upward at a speed of 20.1 m/s, and it hits the ground after an interval of 4.10 s. What is the potential difference between the starting point and the top point of the trajectory? 0.12 m/s 40.2 kv

5 34 The three charges in the figure are at the vertices of an isosceles triangle. Calculate the electric potential at the midpoint of the base, taking q = 7.00 µc. 37 The figure here shows a family of parallel equipotential surfaces (in cross section) and five paths along which we shall move an electron from one surface to another. (a) What is the direction of the electric field associated with the surfaces? (b) For each path, is the work we do positive, negative, or zero? (c) Rank the paths according to the work we do, greatest first x 10 7 V 35 In the figure, a proton moves from point i to point f in a uniform electric field directed as shown. (a) Does the electric field do positive or negative work on the proton? (b) Does the electric potential energy of the proton increase or decrease? (a) rightward (b) 1, 2, 3, 5: positive 4 negative (c) 3, 1,2,5 tied then 4 38 When an electron moves from A to B along an electric field line in the figure, the electric field does 3.94 x J of work on it. (a) What is the electric potential difference V B - V A? (b) What is the electric potential difference V C - V A? (c) What is the electric potential difference V C - V B? (a) negative (b) increase 36 In the figure, we move the proton from point i to point f in a uniform electric field directed as shown. (a) Does our force do positive or negative work? (b) Does the proton move to a point of higher or lower potential? (a) 2.46 V (b) 2.46 V (c) 0 (a) positive (b) higher

6 39 In the figure, particle 1 of charge q 1 = +e and particle 2 of charge q 2 = -5e are fixed on an x axis. Distance d = 5.60?m. What is the electric potential difference V A - V B? 5.14 x 10-4 V 40 Point charges of equal magnitudes (25 nc) and oppo,site signs are placed on diagonally opposite corners of a 60 cm x 80 cm rectangle. Point A is the unoccupied corner nearest the positive charge, and point B is the other unoccupied corner. Determine the potential difference V B - V A V 41 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, and d tie 42 The figure shows three sets of cross sections of equipotential surfaces; all three cover the same size region of space. (a) Rank the arrangements according to the magnitude of the electric field present in the region, greatest first. (b) In which is the electric field directed down the page? (a) 1, then 2 and 3 tie (b) 3