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Figure P23.23 represents the top view of a cubic gaussian surface in a uniform electric field
Figure P23.23
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- Consider a nonconducting sphere and a concentric nonconducting spherical shell, shown in the figure. The inner sphere has non uniform charge density ρ1 = ρ0 / r, where ρ0 is a constant, in units of C/m2 and radius a. The outer spherical shell has uniform charge density ρ2 , inner radius b, and outer radius c. Find the magnitude of the electric field inside the inner sphere, for r < a, in terms of the given variables, as needed.arrow_forwardConsider a spherical Gaussian surface of radius R centered at the origin. A charge Q is placed inside the sphere. Where should the charge be located to maximize the magnitude of the flux of the electric field through the Gaussian surface? A at x = 0, y = R/2, z = 0 B The flux does not depend on the position of the charge as long as it is inside the sphere C) at x = R/2, y = 0, z = 0 D) at x = 0, y = 0, z = R/2arrow_forwardConsider an infinitely long, hollow cylinder, with inner radius R1 and outer radius Ra. the material of the cylinder is uniformly charged so that the cylinder has a charge per length. Finally, consider a solid cylinder of radius R, with a uniform charge density. What is the magnitude of the electric field inside the cylinder at a distance r from the center (r<R)?arrow_forward
- A solid insulating sphere of radius 5 cm carries electric charge uniformly distributed throughout its volume. Concentric with the sphere is a conducting spherical shell with no net charge as shown in Figure OQ24.9. The inner radius of the shell is 10 cm, and the outer radius is 15 cm. No other charges are nearby. (a) Rank the magnitude of the electric Held at points A (at radius 4 cm), B (radius 8 cm), C (radius 12 cm), and I) (radius 16 cm) from largest to smallest. Display any cases of equality in your ranking, (b) Similarly rank the electric flux through concentric spherical surfaces through points A, B. C, and D.arrow_forwardSections AB and CD of a thin non-conducting ring of radius R are uniformly (with constant linear density) charged with charge + q and −q, respectively. The points ABCD form the vertices of the square. Find the electric field in the center of the ring.arrow_forwardA thin nonconducting rod with a uniform distribution of positive charge Q is bent into a circle of radius R (see the figure). The central perpendicular axis through the ring is a z-axis, with the origin at the center of the ring. What is the magnitude of the electric field due to the rod at (a) z = 0 and (b) z = ∞? (c) In terms of R, at what positive value of z is that magnitude maximum? (d) If R = 2.06 cm and Q = 4.33 μC, what is the maximum magnitude?arrow_forward
- A conducting hollow sphere of internal radius a and external b has a total charge + 11q, determine the electric field between radius a and b in terms of ɛ0, q and the radius of the Gaussian r.arrow_forwardA charge distribution that is spherically symmetric but not uniform radially produces an electric field of magnitude E = Kr4, directed radially outward from the center of the sphere. Here r is the radial distance from that center, and K is a constant.What is the volume density r of the charge distribution?arrow_forwardPositive charge Q is distributed uniformly along the x-axis from x=0 to x=a. A positive point charge q is located on the positive x-axis at x=a+r, a distance r to the right of the end of Q. Calculate the x-component of the electric field produced by the charge distribution Q at points on the positive x-axis where x>a. Express your answer in terms of the variables Q, a, r, and and appropriate constants. Calculate the magnitude of the force that the charge distribution Q exerts on q. Express your answer in terms of the variables Q, q, a, r, and appropriate constants. Calculate the direction of the force that the charge distribution Q exerts on q.arrow_forward
- Positive charge Q is distributed uniformly along the x-axis from x=0 to x=a. A positive point charge q is located on the positive x-axis at x=a+r, a distance r to the right of the end of Q. Calculate the x-component of the electric field produced by the charge distribution Q at points on the positive x-axis where x>a. Express your answer in terms of the variables Q, a, r, and and appropriate constants. Calculate the y-component of the electric field produced by the charge distribution Q at points on the positive x-axis where x>a. Express your answer in terms of the variables Q, a, x, and appropriate constants. Calculate the magnitude of the force that the charge distribution Q exerts on q. Express your answer in terms of the variables Q, q, a, r, and appropriate constants. Calculate the direction of the force that the charge distribution Q exerts on q.arrow_forwardA Gaussian surface in the form of a hemisphere of radius R = 5.84 cm lies in a uniform electric field of magnitude E = 2.20 N/C. The surface encloses no net charge. At the (flat) base of the surface, the field is perpendicular to the surface and directed into the surface. (a) What is the flux through the base? ______________N · m2/C(b) What is the flux through the curved portion of the surface? _______________N · m2/Carrow_forwardProblem 6: A circular loop of radius R= 2 cm is centered at the origin where there is a constant electric field E = Egi + Eyj. For this problem, assume E,= 32 N/C and E, = 156 N/C. Part (a) What is the flux through the loop, in Nm2/C, when the loop is oriented so that its normal vector is in the x-direction? Part (b) What is the flux through the loop, in Nm2/C, when the loop is oriented so that its normal vector is in the negative y-direction? = Part (c) What is the flux through the loop, in Nm2/C, when the loop is oriented so that its normal vector is in the positive z-direction?arrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning