Essential University Physics
4th Edition
ISBN: 9780134988566
Author: Wolfson, Richard
Publisher: Pearson Education,
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Chapter 21, Problem 45P
An electric field is given by
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A thin straight infinitely long conducting wire having charge density X is enclosed by a cylindrical surface of radius r and length l, its axis coinciding with the length of the wire. Find the expression for the electric flux through the surface of the cylinder.
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The cube in the figure has edge length 1.87 m and is oriented as shown in a region of uniform electric field. Find the electric flux through the right face if the electric field (a) is in the positive x direction and has magnitude 8.81 N/C, (b) is in the negative y direction and has magnitude 2.22 N/C, and (c) is in the xz plane, has x component -2.75 N/C, and has z component 4.53 N/C. (d) What is the total flux through the cube's surface for each field?
Chapter 21 Solutions
Essential University Physics
Ch. 21.1 - Which figure represents the electric field of a...Ch. 21.2 - The figure shows a cube of side s in a uniform...Ch. 21.3 - A spherical surface surrounds an isolated positive...Ch. 21.4 - A spherical shell carries charge Q distributed...Ch. 21.5 - (1) If you're close to a finite line of charge...Ch. 21.6 - (1) If you're close to a finite line of charge...Ch. 21 - Can electric field lines ever cross? Why or why...Ch. 21 - The electric flux through a closed surface is...Ch. 21 - Under what conditions can the electric flux...Ch. 21 - Right field lines emerge from a closed surface...
Ch. 21 - In Gausss law, EdA=q0does the field E necessarily...Ch. 21 - The field of an infinite charged line decreases as...Ch. 21 - Why cant you use Gausss law to determine the field...Ch. 21 - Youre sitting inside an uncharged, hollow...Ch. 21 - Does Gausss law apply to a spherical Gaussian...Ch. 21 - The electric field of a flat sheet of charge is...Ch. 21 - In Fig. 21.32, the magnitude of the middle charge...Ch. 21 - Charges +2q and q are near each other. Sketch some...Ch. 21 - The net charge shown in Fig. 21.33 is +Q. Identify...Ch. 21 - A flat surface with area 2.0 m2 is in a uniform...Ch. 21 - The electric field on the surface of a...Ch. 21 - In the figure with GOT IT? 21.2, take E = 1.75...Ch. 21 - In Fig. 21.8, take the half-cylinders radius and...Ch. 21 - A sock comes out of the dryer with a trillion...Ch. 21 - Whats the electric flux through the closed...Ch. 21 - Interpret This problem involves applying Gauss's...Ch. 21 - A 2.6-C charge is at the center of a cube 7.5 cm...Ch. 21 - The electric field at the surface of a...Ch. 21 - A solid sphere 25 cm in radius carries 14C,...Ch. 21 - A 15-nC point charge is at the center of a thin...Ch. 21 - The electric field strength outside a charge...Ch. 21 - An electron close to a large, Hat sheet of charge...Ch. 21 - Find the field produced by a uniformly charged...Ch. 21 - What surface charge density on an infinite sheet...Ch. 21 - A rod 50 cm long and 1.0 cm in radius carries a...Ch. 21 - Whats the approximate field strength 1 cm above a...Ch. 21 - The disk in Fig. 21.22 has area 0.14 m2 and is...Ch. 21 - What is the electric field strength just outside...Ch. 21 - A net charge of 5.0 C is applied on one side of a...Ch. 21 - A positive point charge q lies at the center of a...Ch. 21 - A total charge of 18 C is applied to a thin,...Ch. 21 - Example 21.2: A positive point charge +q is at the...Ch. 21 - Example 21.2: A point charge q is at the center of...Ch. 21 - Example 21.2: A long, thin wire carrying uniform...Ch. 21 - Example 21.2: A long, thin wire canning uniform...Ch. 21 - Example 21.4: A long, straight wire carries a...Ch. 21 - Example 21.4: A long, thin rod carries charge...Ch. 21 - Example 21.4: An infinitely long rod carries a...Ch. 21 - Example 21.4: A 75.0-cm-long rod of diameter 2.54...Ch. 21 - Whats the flux through the hemispherical open...Ch. 21 - An electric field is given byE=E0(y/a)k, where E0...Ch. 21 - The electric field in a certain region is given by...Ch. 21 - A study shows that mammalian red blood cells...Ch. 21 - Positive charge is spread uniformly over the...Ch. 21 - A solid sphere 2.0 cm in radius carries a uniform...Ch. 21 - A point charge of 2Q is at the center of a...Ch. 21 - Prob. 51PCh. 21 - A spherical shell of radius R and negligible...Ch. 21 - A spherical shell 30 cm in diameter carries 85 C...Ch. 21 - A thick, spherical shell of inner radius a and...Ch. 21 - A long, thin wire carrying 5.6 nC/m runs down the...Ch. 21 - A long, solid rod of radius R carries a uniform...Ch. 21 - A solid rod 2.54 cm in diameter and 1.50 m long...Ch. 21 - If you painted positive charge on the floor, what...Ch. 21 - A charged slab extends infinitely in two...Ch. 21 - A solid sphere 10 cm in radius carries a 40-C...Ch. 21 - A nonconducting square plate 75 cm on a side...Ch. 21 - A 250-nC point charge is placed at the center of...Ch. 21 - An irregular conductor containing an irregular,...Ch. 21 - You measure the electric field strength at points...Ch. 21 - A point charge q is at the center of a spherical...Ch. 21 - A point charge q is at the center of a spherical...Ch. 21 - The volume charge density inside a solid sphere of...Ch. 21 - Figure 21.37 shows a rectangular box with sides 2a...Ch. 21 - The charge density within a charged sphere of...Ch. 21 - Calculate the electric fields in Example 21.2...Ch. 21 - A solid sphere of radius R carries a nonuniform...Ch. 21 - Problem 76 of Chapter 13 explored what happened to...Ch. 21 - An infinitely long solid cylinder of radius R...Ch. 21 - A solid sphere of radius R carries a uniform...Ch. 21 - Repeal Problem 59 for the case where the charge...Ch. 21 - Coaxial cables are widely used with audio-visual...Ch. 21 - A coaxial cable carries equal but opposite charges...Ch. 21 - How does the electric field between the conductors...Ch. 21 - Coaxial cables are widely used with audio-visual...
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- Consider a plane surface in a uniform electric field as in the Figure , where cm and . If the net flux through the surface is 6.00 Nm2/C, find the magnitude of the electric field.arrow_forwardIf the electric field is given by 6i+3j+4k calculate the electric flux through a surface of area 20 units lying in y-z plane.arrow_forwardCalculate the magnitude of the flux of a constant electric field of 5.00 N/C in the z-direction through a rectangle with area 4.00 m2 in the xy-planearrow_forward
- A flat sheet of paper is cut into an equilateral hexagon that is oriented so that the normal to the sheet is at an angle of 60 degrees to a uniform electric field of magnitude 14 MN/C. If the length of the line formed by joining the first and the fourth vertex is 200 mm, find the magnitude of the electric flux through the sheet.arrow_forwardA point charge qq is at the point x=0,y=0,z=0.x=0,y=0,z=0. An imaginary hemispherical surface is made by starting with a spherical surface of radius RR centered on the point x=0,y=0,z=0x=0,y=0,z=0 and cutting off the half in the region z<0.z<0. The normal to this surface points out of the hemisphere, away from its center. Calculate the electric flux through the hemisphere if (a) q=8.00 nCq=8.00 nC and R=0.100 m;R=0.100 m; (b) q=−4.00 nCq=−4.00 nC and R=0.100 m;R=0.100 m; (c) q=−4.00 nCq=−4.00 nC and R=0.200 m;.arrow_forwardA nonuniform electric field is given by the expression E→ = ay î + bz ĵ + cx k̂where a, b, and c are constants. Determine the electric flux through a rectangular surface in the xy plane, extending from x = 0 to x = w and from y = 0 to y = h.arrow_forward
- In free space, let D = 8xyz4ax + 4x2z4ay + 16x2yz3 az pC/m2.Find the total electric flux passing through the rectangularsurface z = 2, 0 < x < 2, 1 < y < 3, in the az direction. Find Eat P(2, −1, 3).arrow_forwardcalculate the flux of the vector field through the given surface. ~F= (x2−2)~i through a square of side length 3 in the yz-plane, oriented in the negative x-direction.arrow_forwardA solid conducting sphere of radius R has a uniform charge distribution, with a density = Ps * r / R where Ps is a constant and r the distance from the center of the sphere. Prove a) the total charge on the sphere is Q = πPsR ^ 3 b) the electric field of the sphere is given by E = (1 / 4πε0) * (Q / R ^ 4) * (r ^ 2)arrow_forward
- Find the flux through the top, left, and rights sides of a cube of side 0. 3 m when placed in a horizontal uniform electric field of 8.0 N/C directed to the right.arrow_forwardConsider the uniform electric field →E=(4300 j+ 2800 k) NC. What is its electric flux through a circular area of radius 2.4 m that lies in the xy-plane?arrow_forwardFind the electric field at a distance h from the center of a ring of radius R, whose linear charge density is homogeneous and equal to λarrow_forward
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