1. Electric field due to a line of charge A total charge of Q is dis- tributed uniformly on a line segment of length 2L along the y-axis (see figure). The x-component of the electric field at a point (a, 0) is given by kQa dy E,(a) %3D 2L (a² + y?j³/2° where k is a physical constant and a > 0. kQ aVa? + L? b. Letting p = Q/2L be the charge density on the line segment, show that if L→ 0, then E-(a) = 2kp/a. a. Confirm that E,(a) (See the Guided Project Electric field integrals for a derivation of this and other similar integrals.) y. Line of charge (а, 0) -L+

1. Electric field due to a line of charge A total charge of Q is dis- tributed uniformly on a line segment of length 2L along the y-axis (see figure). The x-component of the electric field at a point (a, 0) is given by kQa dy E,(a) %3D 2L (a² + y?j³/2° where k is a physical constant and a > 0. kQ aVa? + L? b. Letting p = Q/2L be the charge density on the line segment, show that if L→ 0, then E-(a) = 2kp/a. a. Confirm that E,(a) (See the Guided Project Electric field integrals for a derivation of this and other similar integrals.) y. Line of charge (а, 0) -L+

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter19: Electric Forces And Electric Fields

Section: Chapter Questions

Problem 52P: A cylindrical shell of radius 7.00 cm and length 2.40 m has its charge uniformly distributed on its...

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A nonconducting, thin plane sheet of charge carries a uniform charge per unit area of 5.20 C/m2 as in Figure 15.30. (a) Find the electric field at a distance of 8.70 cm from the plate. (b) Explain whether your result changes as the distance from the sheet is varied.
Suppose the conducting spherical shell of Figure 15.29 carries a charge of 3.00 nC and that a charge of -2.00 nC is at the center of the sphere. If a = 2.00 m and b = 2.40 m. find the electric field at (a) r = 1.50 m, (b) r = 2.20 m, and (c) r = 2.50 m. (d) What is the charge distribution on the sphere?
A thin, square, conducting plate 50.0 cm on a side lies in the xy plane. A total charge of 4.00 108 C is placed on the plate. Find (a) the charge density on each face of the plate, (b) the electric field just above the plate, and (c) the electric field just below the plate. You may assume the charge density is uniform.
Example 23.3 derives the exact expression for the electric field at a point on the axis of a uniformly charged disk. Consider a disk of radius R = 3.00 cm having a uniformly distributed charge of +5.20 C. (a) Using the result of Example 23.3, compute the electric field at a point on the axis and 3.00 mm from the center. (b) What If? Explain how the answer to part (a) compares with the field computed from the near-field approximation E = /20. (We derived this expression in Example 23.3.) (c) Using the result of Example 23.3, compute the electric field at a point on the axis and 30.0 cm from the center of the disk. (d) What If? Explain how the answer to part (c) compares with the electric field obtained by treating the disk as a +5.20-C charged particle at a distance of 30.0 cm.
A charge of q = 2.00 109 G is spread evenly on a thin metal disk of radius 0.200 m. (a) Calculate the charge density on the disk. (b) Find the magnitude of the electric field just above the center of the disk, neglecting edge effects and assuming a uniform distribution of charge.
(a) Using the symmetry of the arrangement, determine the direction of the electric field at the center of the square in Figure 18.53, given that qa= 1.00C and qc=qd= +1.00 C. (b) Calculate the magnitude of the electric field at the location of q, given that the square is 5.00 cm on a side.
A cylindrical shell of radius 7.00 cm and length 2.40 m has its charge uniformly distributed on its curved surface. The magnitude of the electric field at a point 19.0 cm radially outward from its axis (measured from the midpoint of the shell) is 36.0 kN/C. Find (a) the net charge on the shell and (b) the electric field at a point 4.00 cm from the axis, measured radially outward from the midpoint of the shell.
A solid insulating sphere of radius R has a nonuniform charge density that varies with r according to the expression = Ar2, where A is a constant and r R is measured from the center of the sphere. (a) Show that the magnitude of the electric field outside (r R) the sphere is E = AR5/50r2. (b) Show that the magnitude of the electric field inside (r R) the sphere is E = Ar3/50. Note: The volume element dV for a spherical shell of radius r and thickness dr is equal to 4r2dr.
A long, straight metal rod has a radius of 5.00 cm and a charge per unit length of 30.0 nC/m. Find the electric field (a) 3.00 cm, (b) 10.0 cm. and (c) 100 cm from the axis of the rod, where distances are measured perpendicular to the rods axis.
A spherically symmetric charge distribution has a charge density given by p = a/r; where a is constant. Find the electric field within the charge distribution as a function of r. Note:The volume element dV for a spherical shell of radius r and thickness dr is equal to 4 r2dr.
A particle with charge Q is located on the axis of a circle of radius R at a distance b from the plane of the circle (Fig. P23.48). Show that if one-fourth of the electric flux from the charge passes through the circle, then R=3b. Figure P23.48