25. A continuous line of charge lies along the x axis, extend-ing from x = + x, to positive infinity. The line carries auniform linear charge density Ap. What are the magni-tude and direction of the electric field at the origin?26. A line of charge starts at x = +xg and extends to posi-tive infinity. If the linear charge density is A = Ap xa /x,determine the electric field at the origin.27. A uniformly charged ring of radius 10.0 cm has a totalcharge of 75.0 µC. Find the electric field on the axis ofthe ring at (a) 1.00 cm, (b) 5.00 cm, (c) 30.0 cm, and(d) 100 cm from the center of the ring.28. Show that the maximum field strength Emax along theaxis of a uniformly charged ring occurs at x = a/V2(sce Fig. 23.17) and has the value Q/(6v3me,a*).29. A uniformly charged disk of radius 35.0 cm carries acharge density of 7.90 x 10- C/m?. Calculate theelectric field on the axis of the disk at (a) 5.00 cm,(b) 10.0 cm, (c) 50.0 cm, and (d) 200 cm from the cen-•0Figure P23.33ter of the disk.30. Example 23.9 derives the exact expression for the elec-tric field at a point on the axis of a uniformly chargeddisk. Consider a disk of radius R = 3.00 cm having auniformly distributed charge of + 5.20 µC. (a) Usingthe result of Example 23.9, compute the electric field ata point on the axis and 3.00 mm from the center. Com-pare this answer with the field computed from the near-field approximation E = 0/2€. (b) Using the result ofExample 23.9, compute the electric field at a point onthe axis and 30.0 cm from the center of the disk. Com-dxFigure P23.34carrying the same charge, which is uniformly distrib-uted through its volume. Use the result of Example 23.9to find the field it creates at the same point.35. A thin rod of length € and uniform charge per unitlength à lies along the xaxis, as shown in Figure P23.35.(a) Show that the electric field at P, a distance y fromthe rod, along the perpendicular bisector has no xcom-ponent and is given by E = 2k,A sin 6/y. (b) Usingyour result to part (a), show that the field of a rod of in-finite length is E = 2k,A/y. (Hint: First calculate thefield at Pdue to an element of length dx, which has acharge A dx. Then change variables from x to 6, usingthe facts that x = y tan 0 and dx = y see? 0 do, and inte-pare this result with the electric field obtained by treat-ing the disk as a +5.20-uC point charge at a distance of30.0 ст.31. The electric field along the axis of a uniformly chargeddisk of radius Rand total charge Qwas calculated in Ex-ample 23.9. Show that the electric field at distances xthat are great compared with Rapproaches that of apoint charge Q = onR". (Hint: First show thatx/(x* + R* )!/2 = (1 + R*/x)-1/2, and use the bino-mial expansion (1 + 8)" 1 + nổ when ô« 1.)32. A piece of Styrofoam having a mass m carries a netcharge of – gand floats above the center of a very largehorizontal sheet of plastic that has a uniform chargedensity on its surface. What is the charge per unit areaon the plastic sheet?grate over 0.)WED 33. A uniformly charged insulating rod of length 14.0 cm isbent into the shape of a semicircle, as shown in FigureP23.33. The rod has a total charge of – 7.50 µC. Findthe magnitude and direction of the electric field at 0,the center of the semicirele.34. (a) Consider a uniformly charged right circular cylin-drical shell having total charge Q, radius R, and heighth. Determine the electric field at a point a distance dfrom the right side of the cylinder, as shown in FigureP23.34. (Hint: Use the result of Example 23.8 and treatthe cylinder as a collection of ring charges.) (b) Con-sider now a solid cylinder with the same dimensions anddxFigure P23.3536. Three solid plastic cylinders all have a radius of 2.50 cmand a length of 6.00 cm. One (a) carries charge with 59. Identical thin rods of length 2a carry equal charges,+Q, uniformly distributed along their lengths. Therods lie along the x axis with thcir centers separated bya distance of b> 2a (Fig. P23.59). Show that the magni-tude of the force exerted by the left rod on the rightone is given byIn62 - 4a?F

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A continuous line of charge lies along the x axis, extend- ing from x + x to positive infinity. The line carries a uniform linear charge density A. What are the magni- tude and direction of the electric field at the origin?

A continuous line of charge lies along the x axis, extend- ing from x + x to positive infinity. The line carries a uniform linear charge density A. What are the magni- tude and direction of the electric field at the origin?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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