# Yearly Archives: 2019

41059 posts

## 21.101 In a follow-up experiment a charge of +40 pC was placed at the center of an artificial flower at the end of a 30-cmlong stem. Bees were observed to approach no closer than 15 cm from the center of this flower before they flew away. This observation suggests that the smallest external electric field to which bees may be sensitive is closest to which of these values? (a) 2.4 N>C; (b) 16 N>C; (c) 2.7 * 10-10 N>C; (d) 4.8 * 10-10 N>C.

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## 21.100 After one bee left a flower with a positive charge that bee flew away and another bee with the same amount of positive charge flew close to the plant. Which diagram in Fig. P21.100 best represents the electric field lines between the bee and the flower?

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## 21.99 What is the best explanation for the observation that the electric charge on the stem became positive as the charged bee approached (before it landed)? (a) Because air is a good conductor the positive charge on the bee’s surface flowed through the air from bee to plant. (b) Because the earth is a reservoir of large amounts of charge positive ions were drawn up the stem from the ground toward the charged bee. (c) The plant became electrically polarized as the charged bee approached. (d) Bees that had visited the plant earlier deposited a positive charge on the stem.

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## 21.98 Consider a bee with the mean electric charge found in the experiment. This charge represents roughly how many missing electrons? (a) 1.9 * 108; (b) 3.0 * 108; (c) 1.9 * 1018; (d) 3.0 * 1018.

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## 21.97 … CALC Two thin rods of length L lie along the x-axis one between x = 12 a and x = 12 a + L and the other between x = -12 a and x = -12 a – L. Each rod has positive charge Q distributed uniformly along its length. (a) Calculate the electric field produced by the second rod at points along the positive x-axis. (b) Show that the magnitude of the force that one rod exerts on the other is

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## 21.96 … Two charges are placed as shown in Fig. P21.96. The magnitude of q1 is 3.00 mC but its sign and the value of the charge q2 are not known. The direction of the net electric field E S at point P is entirely in the negative y-direction. (a) Considering the different possible signs of q1 and q2 four possible diagrams could represent the electric fields E S 1 and E S 2 produced by q1 and q2. Sketch the four possible electric-field configurations. (b) Using the sketches from part (a) and the direction of E S deduce the signs of q1 and q2 . (c) Determine the magnitude of E S .

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## 21.95 … Three charges are placed as shown in Fig. P21.95. The magnitude of q1 is 2.00 mC but its sign and the value of the charge q2 are not known. Charge q3 is +4.00 mC and the net force F S on q3 is entirely in the negative x-direction. (a) Considering the different possible signs of q1 there are four possible force diagrams representing the forces F S 1 and F S 2 that q1 and q2 exert on q3 . Sketch these four possible force configurations. (b) Using the sketches from part (a) and the direction of F S deduce the signs of the charges q1 and q2 . (c) Calculate the magnitude of q2 . (d) Determine F the magnitude of the net force on q3 .

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## 21.94 … DATA Positive charge Q is distributed uniformly around a very thin conducting ring of radius a as in Fig. 21.23. You measure the electric field E at points on the ring axis at a distance x from the center of the ring over a wide range of values of x. (a) Your results for the larger values of x are plotted in Fig. P21.94a as Ex2 versus x. Explain why the quantity Ex2 approaches a constant value as x increases. Use Fig. P21.94a to calculate the net charge Q on the ring. (b) Your results for smaller values of x are plotted in Fig. P21.94b as E>x versus x. Explain why E>x approaches a constant value as x approaches zero. Use Fig. P21.94b to calculate a.

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## 21.93 .. DATA Two small spheres each carrying a net positive charge are separated by 0.400 m. You have been asked to perform measurements that will allow you to determine the charge on each sphere. You set up a coordinate system with one sphere (charge q1) at the origin and the other sphere (charge q2) at x = +0.400 m. Available to you are a third sphere with net charge q3 = 4.00 * 10-6 C and an apparatus that can accurately measure the location of this sphere and the net force on it. First you place the third sphere on the x@axis at x = 0.200 m; you measure the net force on it to be 4.50 N in the +x@direction. Then you move the third sphere to x = +0.600 m and measure the net force on it now to be 3.50 N in the +x@direction. (a) Calculate q1 and q2. (b) What is the net force (magnitude and direction) on q3 if it is placed on the x@axis at x = -0.200 m? (c) At what value of x (other than x = {q) could q3 be placed so that the net force on it is zero?

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## 21.92 … DATA CP Design of an Inkjet Printer. Inkjet printers can be described as either continuous or drop-on-demand. In a continuous inkjet printer letters are built up by squirting drops of ink at the paper from a rapidly moving nozzle. You are part of an engineering group working on the design of such a printer. Each ink drop will have a mass of 1.4 * 10-8 g. The drops will leave the nozzle and travel toward the paper at 50 m>s passing through a charging unit that gives each drop a positive charge q by removing some electrons from it. The drops will then pass between parallel deflecting plates 2.0 cm long where there is a uniform vertical electric field with magnitude 8.0 * 104 N>C. Your team is working on the design of the charging unit that places the charge on the drops. (a) If a drop is to be deflected 0.30 mm by the time it reaches the end of the deflection plates what magnitude of charge must be given to the drop? How many electrons must be removed from the drop to give it this charge? (b) If the unit that produces the stream of drops is redesigned so that it produces drops with a speed of 25 m>s what q value is needed to achieve the same 0.30-mm deflection?

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## 21.91 .. CP A thin disk with a circular hole at its center called an annulus has inner radius R1 and outer radius R2 (Fig. P21.91). The disk has a uniform positive surface charge density s on its surface. (a) Determine the total electric charge on the annulus. (b) The annulus lies in the yz-plane with its center at the origin. For an arbitrary point on the x-axis (the axis of the annulus) find the magnitude and direction of the electric field E S . Consider points both above and below the annulus. (c) Show that at points on the x-axis that are sufficiently close to the origin the magnitude of the electric field is approximately proportional to the distance between the center of the annulus and the point. How close is “sufficiently close”? (d) A point particle with mass m and negative charge -q is free to move along the x-axis (but cannot move off the axis). The particle is originally placed at rest at x = 0.01 R1 and released. Find the frequency of oscillation of the particle. (Hint: Review Section 14.2. The annulus is held stationary.)

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## 21.90 . Two very large horizontal sheets are 4.25 cm apart and carry equal but opposite uniform surface charge densities of magnitude s. You want to use these sheets to hold stationary in the region between them an oil droplet of mass 486 mg that carries an excess of five electrons. Assuming that the drop is in vacuum (a) which way should the electric field between the plates point and (b) what should s be?

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## 21.89 . Repeat Problem 21.88 for the case where sheet B is positive.

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## 21.88 . Two very large parallel sheets are 5.00 cm apart. Sheet A carries a uniform surface charge density of -8.80 mC>m2 and sheet B which is to the right of A carries a uniform charge density of -11.6 mC>m2. Assume that the sheets are large enough to be treated as infinite. Find the magnitude and direction of the net electric field these sheets produce at a point (a) 4.00 cm to the right of sheet A; (b) 4.00 cm to the left of sheet A; (c) 4.00 cm to the right of sheet B.

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## 21.87 .. Two 1.20@m nonconducting rods meet at a right angle. One rod carries +2.50 mC of charge distributed uniformly along its length and the other carries -2.50 mC distributed uniformly along it (Fig. P21.87). (a) Find the magnitude and direction of the electric field these rods produce at point P which is 60.0 cm from each rod. (b) If an electron is released at P what are the magnitude and direction of the net force that these rods exert on it?

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## 21.86 .. CALC A semicircle of radius a is in the first and second quadrants with the center of curvature at the origin. Positive charge +Q is distributed uniformly around the left half of the semicircle and negative charge -Q is distributed uniformly around the right half of the semicircle (Fig. P21.86). What are the magnitude and direction of the net electric field at the origin produced by this distribution of charge?

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## 21.85 .. CALC Negative charge -Q is distributed uniformly around a quarter-circle of radius a that lies in the first quadrant with the center of curvature at the origin. Find the x- and y-components of the net electric field at the origin.

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## 21.84 .. CP A small sphere with mass m carries a positive charge q and is attached to one end of a silk fiber of length L. The other end of the fiber is attached to a large vertical insulating sheet that has a positive surface charge density s. Show that when the sphere is in equilibrium the fiber makes an angle equal to arctan 1qs>2mgP02 with the vertical sheet.

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## 21.83 … A uniformly charged disk like the disk in Fig. 21.25 has radius 2.50 cm and carries a total charge of 7.0 * 10-12 C. (a) Find the electric field (magnitude and direction) on the x-axis at x = 20.0 cm. (b) Show that for x W R Eq. (21.11) becomes E = Q>4pP0 x2 where Q is the total charge on the disk. (c) Is the magnitude of the electric field you calculated in part (a) larger or smaller than the electric field 20.0 cm from a point charge that has the same total charge as this disk? In terms of the approximation used in part (b) to derive E = Q>4pP0 x2 for a point charge from Eq. (21.11) explain why this is so. (d) What is the percent difference between the electric fields produced by the finite disk and by a point charge with the same charge at x = 20.0 cm and at x = 10.0 cm?

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## 21.82 .. CALC Positive charge Q is distributed uniformly along the positive y-axis between y = 0 and y = a. A negative point charge -q lies on the positive x-axis a distance x from the origin (Fig. P21.82). (a) Calculate the x- and y-components of the electric field produced by the charge distribution Q at points on the positive x-axis. (b) Calculate the x- and y-components of the force that the charge distribution Q exerts on q. (c) Show that if x W a Fx _ -Qq>4pP0 x2 and Fy _ +Qqa>8pP0 x3. Explain why this result is obtained.

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## 21.81 . A negative point charge q1 = -4.00 nC is on the x-axis at x = 0.60 m. A second point charge q2 is on the x-axis at x = -1.20 m. What must the sign and magnitude of q2 be for the net electric field at the origin to be (a) 50.0 N>C in the +x@direction and (b) 50.0 N>C in the -x@direction?

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## 21.80 .. In a region where there is a uniform electric field that is upward and has magnitude 3.60 * 104 N>C a small object is projected upward with an initial speed of 1.92 m>s. The object travels upward a distance of 6.98 cm in 0.200 s. What is the object’s chargeto- mass ratio q>m? Assume g = 9.80 m>s2 and ignore air resistance.

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## 21.79 .. CALC Positive charge Q is distributed uniformly along the x-axis from x = 0 to x = a. A positive point charge q is located on the positive x-axis at x = a + r a distance r to the right of the end of Q (Fig. P21.79). (a) Calculate the x- and y-components of the electric field produced by the charge distribution Q at points on the positive x-axis where x 7 a. (b) Calculate the force (magnitude and direction) that the charge distribution Q exerts on q. (c) Show that if r W a the magnitude of the force in part (b) is approximately Qq>4pP0 r2. Explain why this result is obtained.

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## 21.78 … A small object with mass m charge q and initial speed v0 = 5.00 * 103 m>s is projected into a uniform electric field between two parallel metal plates of length 26.0 cm (Fig. P21.78). The electric field between the plates is directed downward and has magnitude E = 800 N>C. Assume that the field is zero outside the region between the plates. The separation between the plates is large enough for the object to pass between the plates without hitting the lower plate. After passing through the field region the object is deflected downward a vertical distance d = 1.25 cm from its original direction of motion and reaches a collecting plate that is 56.0 cm from the edge of the parallel plates. Ignore gravity and air resistance. Calculate the object’s charge-to-mass ratio q>m.

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## 21.77 .. CP A proton is projected into a uniform electric field that points vertically upward and has magnitude E. The initial velocity of the proton has a magnitude v0 and is directed at an angle a below the horizontal. (a) Find the maximum distance hmax that the proton descends vertically below its initial elevation. Ignore gravitational forces. (b) After what horizontal distance d does the proton return to its original elevation? (c) Sketch the trajectory of the proton. (d) Find the numerical values of hmax and d if E = 500 N>C v0 = 4.00 * 105 m>s and a = 30.0_.

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## 21.76 .. The earth has a downward-directed electric field near its surface of about 150 N>C. If a raindrop with a diameter of 0.020 mm is suspended motionless in this field how many excess electrons must it have on its surface?

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## 21.75 .. CP Consider a model of a hydrogen atom in which an electron is in a circular orbit of radius r = 5.29 * 10-11 m around a stationary proton. What is the speed of the electron in its orbit?

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