What does "uniform" mean in the context of charge distributions? O The electrostatic force exerted by the charge distribution on the test charge is always attractive, never repulsive. O The answer cannot be found on the other choices. O The charge is distributed evenly throughout the line, surface, or volume. O The electric field being produced by the charge distribution is always constant everywhere.

What does "uniform" mean in the context of charge distributions? O The electrostatic force exerted by the charge distribution on the test charge is always attractive, never repulsive. O The answer cannot be found on the other choices. O The charge is distributed evenly throughout the line, surface, or volume. O The electric field being produced by the charge distribution is always constant everywhere.

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter25: Gauss’s Law

Section: Chapter Questions

Problem 78PQ

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Often we have distributions of charge for which integrating to find the electric field may not be possible in practice. In such cases, we may be able to get a good approximate solution by dividing the distribution into small but finite particles and taking the vector sum of the contributions of each. To see how this might work, consider a very thin rod of length L = 16 cm with uniform linear charge density = 50.0 nC/m. Estimate the magnitude of the electric field at a point P a distance d = 8.0 cm from the end of the rod by dividing it into n segments of equal length as illustrated in Figure P24.21 for n = 4. Treat each segment as a particle whose distance from point P is measured from its center. Find estimates of EP for n = 1, 2, 4, and 8 segments. FIGURE P24.21
A coaxial cable is formed by a long, straight wire and a hollow conducting cylinder with axes that coincide. The wire has charge per unit length = 20, and the hollow cylinder has net charge per unit length = 30. Use Gausss law to answer these questions: What are the charges per unit length on a. the inner surface and b. the outer surface of the hollow cylinder? c. What is the electric field a radial distance d from the axis of the coaxial cable?
A very long, thin wire fixed along the x axis has a linear charge density of 3.2 C/m. a. Determine the electric field at point P a distance of 0.50 m from the wire. b. If there is a test charge q0 = 12.0 C at point P, what is the magnitude of the net force on this charge? In which direction will the test charge accelerate?
A solid sphere of radius R has a spherically symmetrical, nonuniform volume charge density given by (r) = A/r, where r is the radial distance from the center of the sphere in meters, and A is a constant such that the density has dimensions of M/L3. Sketch a graph of the magnitude of the electric field as a function of distance for 0 r 3R.
A solid sphere of radius R has a spherically symmetrical, nonuniform volume charge density given by (r) = A/r, where r is the radial distance from the center of the sphere in meters, and A is a constant such that the density has dimensions M/L3. a. Calculate the total charge in the sphere. b. Using the answer to part (a), write an expression for the magnitude of the electric field outside the spherethat is, for some distance r R. c. Find an expression for the magnitude of the electric field inside the sphere at position r R.
A sphere with radius R has a charge density given by = cr3. Use Gausss law to find an expression for the magnitude of the electric field at a distance r from the center of the sphere, where a. r R and b. r R.
(a) Consider a uniformly charged, thin-walled, right circular cylindrical shell having total charge Q , radius R, and length l. Determine the electric field at a point a distance d from the right side of the cylinder as shown in the Figure. Suggestion: treat the cylinder as a collection of ring charges. (b) Consider now a solid cylinder with the same dimensions and carrying the same charge,uniformly distributed through its volume.
(a) Consider a uniformly charged, thin-walled, right circular cylindrical shell having total charge Q, radius R, and length ℓ. Determine the electric field at a point a distance d from the right side of the cylinder as shown. Suggestion: Use the result of Example 23.2 and treat the cylinder as a collection of ring charges. (b) What If? Consider now a solid cylinder with the same dimensions and carrying the same charge, uniformly distributed through its volume. Use the result of Example 23.3 to find the field it creates at the same point.
(a) Consider a uniformly charged, thin-walled, right circular cylindrical shell having total charge ,Q radius R and length Determine the electric field at a point a distance from the right side of the cylinder as shown in Figure Suggestion: Use the result of Example 23.7 and treat the cylinder as a collection of ring charges. (b) What If? Consider now a solid cylinder with the same dimensions and carrying the same charge, uniformly distributed through its volume. Use the result of Example 23.8 to find the field it creates at the same point.
(a) A rod of length 2L with uniform charge density λ is oriented along the z-axis, centered at z = 0. Find the electric field at any point on the xy plane a distance r from the rod. (Note that the figure corresponds to part c only). (b) Use your result from the previous part to show that the electric field a distance r from an infinite rod is 2λ 4πǫ0r . (c) Suppose a section with length 2L is cut out of the infinite rod. Let the center of the cut out section correspond to z = 0 as shown. Find the E-field a distance r from the z-axis in the x-y plane.
a. Calculate the electric field force on an α Particle at the surface a gold atom presuming that the +ive charge in spread uniformly through the volum of the atom. Ignore the atomic is es. A gold atom has a radius of 0.16nm.treat the α- particle as point particle.b. through what distance would this force, presumed constant have to act to rest? Express your answer in term of the diameter of the gold atom?
(a) A solid sphere, made of an insulating material, has a volume charge density of ρ = a/r, where r is the radius from the center of the sphere, a is constant, and a > 0. What is the electric field within the sphere as a function of the radius r? Note: The volume element dV for a spherical shell of radius r and thickness dr is equal to 4πr2dr. (Use the following as necessary: a, r, and ε0.) magnitude E=________ direction: radially outward, radially inward, or no direction? (b) What If? What if the charge density as a function of r within the charged solid sphere is given by ρ = a/r2? Find the new magnitude and direction of the electric field within the sphere at radius r. (Use the following as necessary: a, r, and ε0.) magnitude E=_________ direction: radially outward, radially inward, or no direction?