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**QUICK QUIZ 25.1 (For the end of section 25.2)**

A uniform electric field points in the positive x direction, as shown below (left). Along the two lines, 1 and 2, a plot of the electric potentials as a function of distance along these lines from initial point i to final point f is best described by which plot below?

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QUICK QUIZ 25.1 ANSWER (c). Since electric field lines point in the direction of decreasing electric potential, the potential decreases as one travels from initial point to final point on each line. Since the electric field is uniform and in the x direction, equipotential lines will be perpendicular to the x axis. Therefore, since the final position of each line has the same x coordinate, each will have the same final potential. Plot c best describes this situation.

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**QUICK QUIZ 25.2 (For the end of section 25.2)**

In a similar experiment to that shown in Figure 23.26, an electron is projected horizontally at a speed vi into a uniform electric field pointing up. The experiment is repeated twice with the electron projected at the same initial speed vi but at angles above and below the horizontal. The path of the electron in each case is shown in the diagram below. The relationship between the final speeds of the electron when it exits the area of the uniform electric field is: a) vb > v > va b) va > v > vb c) vb = va > v d) vb = v = va

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QUICK QUIZ 25.2 ANSWER (a). The initial kinetic energy is the same in each case. This kinetic energy will increase as the electron loses potential energy as it travels towards the positive plate. The loss of potential energy is determined by Equation 25.3: DV = DU/qo. Since the change of potential is determined by the vertical deflection of the electron, the greatest change in potential and potential energy will occur for the case with the maximum vertical deflection from the initial position. As illustrated in the diagram, this occurs when the electron is projected at an angle below the horizontal.

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**QUICK QUIZ 25.3 (For the end of section 25.4)**

In a certain region of space, suppose that the electric potential as a function of position along a certain direction is described by the plot below (left). The electric field as a function of position over the same region of space would best be described which plot?

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QUICK QUIZ 25.3 ANSWER (b). The electric field is the negative derivative of the electric potential as shown by Equation 25.16, Ex = -dV/dx. If the potential is constant in a certain region of space, the electric field must be zero. If the potential is linear with distance with a positive slope, this implies that the electric field is constant and negative. If there is a discontinuity in the potential at some point, this implies that the electric field must be infinite there. Notice that for the examples shown in this chapter, the potential is always continuous.

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**QUICK QUIZ 25.4 (For the end of section 25.5)**

Consider the electric potential near a uniform line of positive charge, as shown in the figure below. You measure the potential at point P. If you then double the length of the line to 2 (while keeping the left end of the line directly below point P) and double the total charge to 2Q, the electric potential you would measure at point P would a) also double, b) more than double, c) remain constant, d) decrease by a factor of two, e) decrease by more than a factor of two, f) increase by less than double, or g) decrease by less than a factor of two.

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QUICK QUIZ 25.4 ANSWER (f). Doubling the length and the total charge would be equivalent to placing a second line of charge to the right of the original line of charge. The potential would increase due to this second line of charge but it would not double since the second line would be farther from point P than the first line of charge. By examining Equation 25.25, you should be able to reach a similar conclusion.

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**QUICK QUIZ 25.5 (For the end of section 25.8)**

In an impromptu home physics experiment, you walk over to the door knob while scuffing your shoes on the carpet and examine the spark that jumps from your finger to the knob. You then repeat the experiment while holding a metal needle and examine the spark that jumps from the needle to the knob. The length of the spark (the separation distance before a spark occurs) will be a) greater while holding the needle, b) less while holding the needle, c) the same in both cases, or d) either greater, less, or the same, dependent on the type of metal.

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QUICK QUIZ 25.5 ANSWER (b). When you scuff your feet across the carpet, charge will build up on you and this charge will discharge through the air onto another object. You must get close enough to the object so that the electric field in the space between is sufficient to cause electric breakdown in the air. When you hold a needle or other metal object with a point, the electric field at the point is sufficient to ionize the air and allow a slow discharge. In fact, while holding a needle, the charge may dissipate from you to enough of an extent that when you reach the knob, the little charge left will produce a spark only when the needle is extremely close to the knob. You may verify this through experiment. Lightning rods work in the same way. They are pointed metal rods that are grounded and they slowly bleed off charge that would otherwise build up and produce a bolt of lightning.

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