Concept explainers
(a)
The expression for the electric field at point A located at a distance l above the mid-point of the rod.
(a)
Answer to Problem 79PQ
The expression for the electric field at point A located at a distance l above the mid-point of the rod is
Explanation of Solution
Sketch the diagram showing the five charges.
The x component of the electric field is zero based on the geometry.
Write the expression for the y component of the electric field.
Here,
Write the equation for the total electric field.
Conclusion:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute equations (III), (IV), (V), (VI) and (VII) in equation (II) to find
Thus, the expression for the electric field at point A located at a distance l above the mid-point of the rod is
(b)
The electric field at point A located at a distance l above the mid-point of the rod using the exact expression.
(b)
Answer to Problem 79PQ
The electric field at point A located at a distance l above the mid-point of the rod using the exact expression is
Explanation of Solution
Write the exact expression for the total electric field.
Here,
Conclusion:
Substitute
Thus, the electric field at point A located at a distance l above the mid-point of the rod using the exact expression is
(c)
Compare the approximate result with the exact result.
(c)
Answer to Problem 79PQ
The approximate result is
Explanation of Solution
Find the ratio of the approximate result with the exact result.
Conclusion:
Thus, the approximate result is
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Chapter 24 Solutions
Physics for Scientists and Engineers: Foundations and Connections, Advance Edition, Volume 2
- A uniformly charged conducting rod of length = 30.0 cm and charge per unit length = 3.00 105 C/m is placed horizontally at the origin (Fig. P24.37). What is the electric field at point A with coordinates (0, 0.400 m)?arrow_forwardA conducting rod carrying a total charge of +9.00 C is bent into a semicircle of radius R = 33.0 cm, with its center of curvature at the origin (Fig.P24.75). The charge density along the rod is given by = 0 sin , where is measured clockwise from the +x axis. What is the magnitude of the electric force on a 1.00-C charged particle placed at the origin?arrow_forwardFind an expression for the magnitude of the electric field at point A mid-way between the two rings of radius R shown in Figure P24.30. The ring on the left has a uniform charge q1 and the ring on the right has a uniform charge q2. The rings are separated by distance d. Assume the positive x axis points to the right, through the center of the rings. FIGURE P24.30 Problems 30 and 31.arrow_forward
- A total charge Q is distributed uniformly on a metal ring of radius R. a. What is the magnitude of the electric field in the center of the ring at point O (Fig. P24.61)? b. What is the magnitude of the electric field at the point A lying on the axis of the ring a distance R from the center O (same length as the radius of the ring)? FIGURE P24.61arrow_forwardA uniform electric field given by E=(2.655.35j)105N/C permeates a region of space in which a small negatively charged sphere of mass 1.30 g is suspended by a light cord (Fig. P24.53). The sphere is found to be in equilibrium when the string makes an angle = 23.0. a. What is the charge on the sphere? b. What is the magnitude of the tension in the cord? FIGURE P24.53arrow_forwardA solid insulating sphere of radius a = 5.00 cm carries a net positive charge of Q = 3.00 C uniformly distributed throughout its volume. Concentric with this sphere is a conducting spherical shell with inner radius b = 10.0 cm and outer radius c = 15.0 cm as shown in Figure P24.54, having net charge q = 1.00 C Prepare a graph of the magnitude of the electric field due to this configuration versus r for O r 25.0 cm.arrow_forward
- If the curved rod in Figure P24.32 has a uniformly distributed charge Q = 35.5 nC, radius R = 0.785 m, and = 60.0, what is the magnitude of the electric field at point A?arrow_forwardA When we find the electric field due to a continuous charge distribution, we imagine slicing that source up into small pieces, finding the electric field produced by the pieces, and then integrating to find the electric field. Lets see what happens if we break a finite rod up into a small number of finite particles. Figure P24.77 shows a rod of length 2 carrying a uniform charge Q modeled as two particles of charge Q/2. The particles are at the ends of the rod. Find an expression for the electric field at point A located a distance above the midpoint of the rod using each of two methods: a. modeling the rod with just two particles and b. using the exact expression E=kQy12+y2 c. Compare your results to the exact expression for the rod by finding the ratio of the approximate expression to the exact expression. FIGURE P24.77 Problems 77 and 78.arrow_forwardIn Figure P24.49, a charged particle of mass m = 4.00 g and charge q = 0.250 C is suspended in static equilibrium at the end of an insulating thread that hangs from a very long, charged, thin rod. The thread is 12.0 cm long and makes an angle of 35.0 with the vertical. Determine the linear charge density of the rod. FIGURE P24.49arrow_forward
- Eight small conducting spheres with identical charge q = 2.00 C are placed at the corners of a cube of side d = 0.500 m (Fig. P23.75). What is the total force on the sphere at the origin (sphere A) due to the other seven spheres? Figure P23.75arrow_forwardA uniformly charged disk with radius R = 35.0 cm and uniform charge density ? = 7.10 ✕ 10−3 C/m2 lies in the xy-plane, with its center at the origin. What is the electric field (in MN/C) due to the charged disk at the following locations? (a) z = 5.00 cm MN/C (b) z = 10.0 cm Use the equation for the electric field for a disk derived in the textbook. MN/C (c) z = 50.0 cm MN/C (d) z = 200 cm MN/Carrow_forwardFive charged particles are equally spaced around a semicircle of radius 100 mm, with one particle at each end of the semicircle and the remaining three spaced equally between the two ends. The semicircle lies in the region x<0 of an xy plane, such that the complete circle is centered on the origin. If each particle carries a charge of 6.00 nC , what is the electric field at the origin? Where could you put a single particle carrying a charge of -5.00 nC to make the electric field magnitude zero at the origin?arrow_forward
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