Concept explainers
(a)
The magnitude of the electric field at a distance
(a)
Answer to Problem 44PQ
The magnitude of the electric field at a distance
Explanation of Solution
Write the expression to find the charge enclosed.
Here,
Write the expression for Gauss’s Law for a spherical symmetry.
Here,
Conclusion:
Substitute
Substitute
Substitute
Therefore, the magnitude of the electric field at a distance
(b)
The magnitude of the electric field at a distance
(b)
Answer to Problem 44PQ
The magnitude of the electric field at a distance
Explanation of Solution
Write the expression for Gauss’s Law for a spherical symmetry.
Here,
Conclusion:
Substitute
Therefore, the magnitude of the electric field at a distance
(c)
The magnitude of the electric field at a distance
(c)
Answer to Problem 44PQ
The magnitude of the electric field at a distance
Explanation of Solution
Write the expression for Gauss’s Law for a spherical symmetry.
Here,
Conclusion:
Substitute
Therefore, the magnitude of the electric field at a distance
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Chapter 25 Solutions
Physics for Scientists and Engineers: Foundations and Connections
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- (a) Determine the electric field strength at a point 1.00 cm to the left of the middle charge shown in Figure P15.10. (b) If a charge of 2.00 C is placed at this point, what are the magnitude and direction of the force on it?arrow_forward(a) Determine the electric field strength at a point 1.00 cm to the left of the middle charge shown in Figure P15.10. (b) If a charge of 2.00 C is placed at this point, what are the magnitude and direction of the force on it?arrow_forwardA 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.arrow_forward
- A solid, insulating sphere of radius a has a uniform charge density throughout its volume and a total charge Q. Concentric with this sphere is an uncharged, conducting, hollow sphere whose inner and outer radii are b and c as shown in Figure P19.75. We wish to understand completely the charges and electric fields at all locations. (a) Find the charge contained within a sphere of radius r a. (b) From this value, find the magnitude of the electric field for r a. (c) What charge is contained within a sphere of radius r when a r b? (d) From this value, find the magnitude of the electric field for r when a r b. (e) Now consider r when b r c. What is the magnitude of the electric field for this range of values of r? (f) From this value, what must be the charge on the inner surface of the hollow sphere? (g) From part (f), what must be the charge on the outer surface of the hollow sphere? (h) Consider the three spherical surfaces of radii a, b, and c. Which of these surfaces has the largest magnitude of surface charge density?arrow_forwardThe infinite sheets in Figure P25.47 are both positively charged. The sheet on the left has a uniform surface charge density of 48.0 C/m2, and the one on the right has a uniform surface charge density of 24.0 C/m2. a. What are the magnitude and direction of the net electric field at points A, B, and C? b. What is the force exerted on an electron placed at points A, B, and C? FIGURE P25.47arrow_forwardA uniformly charged rod of length L and total charge Q lies along the x axis as shown in Figure P23.6. (a) Find the components of the electric field at the point P on the y axis a distance d from the origin. (b) What are the approximate values of the field components when d L? Explain why you would expect these results. Figure P23.6arrow_forward
- Figure P24.51 shows four small charged spheres arranged at the corners of a square with side d = 25.0 cm. a. What is the electric field at the location of the sphere with charge +2.00 nC? b. What is the total electric force exerted on the sphere with charge +2.00 nC by the other three spheres? FIGURE P24.51arrow_forwardA slab of insulating material has a nonuniform positive charge density = Cx2, where x is measured from the center of the slab as shown in Figure P23.45 and C is a constant. The slab is infinite in the y and z directions. Derive expressions for the electric field in (a) the exterior regions (|x| d/2) and (b) the interior region of the slab (d/2 x d/2). Figure P23.45arrow_forward(a) What magnitude point charge creates a 10,000 N/C electric field at a distance of 0.250 m? (b) How large is the field at 10.0 m?arrow_forward
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