(a) A conducting sphere has charge Q and radius R. If theelectric field of the sphere at a distance r = 2R from the center of thesphere is 1400 N/C, what is the electric field of the sphere at r = 4R?(b) A very long conducting cylinder of radius R has charge per unitlength l. Let r be the perpendicular distance from the axis of the cylinder.If the electric field of the cylinder at r = 2R is 1400 N/C, whatis the electric field at r = 4R? (c) A very large uniform sheet of chargehas surface charge density s. If the electric field of the sheet has a valueof 1400 N>C at a perpendicular distance d from the sheet, what is theelectric field of the sheet at a distance of 2d from the sheet?

(a) A conducting sphere has charge Q and radius R. If theelectric field of the sphere at a distance r = 2R from the center of thesphere is 1400 N/C, what is the electric field of the sphere at r = 4R?(b) A very long conducting cylinder of radius R has charge per unitlength l. Let r be the perpendicular distance from the axis of the cylinder.If the electric field of the cylinder at r = 2R is 1400 N/C, whatis the electric field at r = 4R? (c) A very large uniform sheet of chargehas surface charge density s. If the electric field of the sheet has a valueof 1400 N>C at a perpendicular distance d from the sheet, what is theelectric field of the sheet at a distance of 2d from the sheet?

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 43PQ: The nonuniform charge density of a solid insulating sphere of radius R is given by = cr2 (r R),...

See similar textbooks

Similar questions

Two parallel conducting plates, each of cross-sectional area 400 cm2, are 2.0 cm apart and uncharged. If 1.01012 electrons are transferred from one plate to the other, what are (a) the charge density on each plate? (b) The electric field between the plates?
The nonuniform charge density of a solid insulating sphere of radius R is given by = cr2 (r R), where c is a positive constant and r is the radial distance from the center of the sphere. For a spherical shell of radius r and thickness dr, the volume element dV = 4r2dr. a. What is the magnitude of the electric field outside the sphere (r R)? b. What is the magnitude of the electric field inside the sphere (r R)?
The surface charge density on a long straight metallic pipe is . What is the electric field outside and inside the pipe? Assume the pipe has a diameter of 2a.
Positive electric charge Q is distributed uniformly throughout the volume of an insulating sphere with radius R. Find the magnitude of the electric field at a point P a distance r from the center of the sphere.
A solid cylinder has radius 7.77 m and height 7.06 m. If the total charge equally distributed throughout the volume of the cylinder is 15.75 nC, determine the magnitude of the electric field, in volts per meter, 3.24 m radially away from the axis of the cylinder. Express your answers accurate to four decimal places.
A solid conducting sphere of radius R carries a positive electric charge Q. For what values or r is the electric field, E(r) = 0?
s of the 15.13 The Coaxial Cable. A long coaxial cable con- sists of an inner cylindrical conductor with radius a and an outer coaxial cylinder with inner radius b and outer eld also radius c. The outer cylinder is mounted on insulating supports and has no net charge. The inner cylinder has a uniform positive charge per unit length A. Calculate the electric field a) at any point between the cylinders, a distance r from the axis; b) at any point outside the outer cylinder. c) Graph the magnitude of the electric field as a function of the distance r from the axis of the cable, from r=0 to r = 2c. d) Find the charge per unit length on the inner surface and on the outer surface of -ntained by the can you %3D the outer cylinder.
Find the electric field at the origin of the x,y-plane for charge distributions (a) and (b), see the figures shown below. The field is produced (a) by a thin half-circle with a radius of 15 cm and the linear charge density K-10 pc/cm and (b) by a thin quarter-circle with the same radius and the linear charge density K = -10 pc/cm. K>0 (a) For the charge distribution (a): The x-component of Ea. Ea,x= The y-component of Ea, Ea,y= For the charge distribution (b): The x-component of Eb, Eb,x- The y-component of Eb, Eb,y = Units N/C Units N/C Units N/C Units N/C K<0 (b)
This is an equation for an radially directed, electric field of a rod that has finite charge and is uniform. r is the distance of the charge in a plane that bisects the rod. L= length of the rod, Q= Total charge of the rod, k=coulomb's constant. if k=1 units, Q=1 units, L=12 units, what is Erod when r=4?
Consider a thin rod which has a uniformly distributed charge Qot = -1 µC. The rod is bent into a quarter of a circle of radius R = 1 m. Find the x- and y-components of the electric field created by the rod the point O the center of the arc. Hint: The following integrals are useful: cose de = [sin@]% î sine de = [-cos0]% R
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 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.
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.