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P2. A uniformly-charged sphere of radius R is placed near a uniformly-charged long cylinder of radius...
1. A very long, uniformly charged cylinder has radius R and charge density p. Determine the...
1. A very long, uniformly charged cylinder has radius R and charge density \rho. Determine the electric field of this cylinder inside (r<R) and outside (r>R)2. A large, flat, nonconducting surface carries a uniform surface charge density σ. A small circular hole of radius R has been cut in the middle of the sheet. Determine the electric field at a distance z directly above the center of the hole.3. You have a solid, nonconducting sphere that is inside of, and...
A very long solid non-conducting cylinder of radius R1 is uniformly charged with a charge density p.
A very long solid non-conducting cylinder of radius R1 is uniformly charged with a charge density p. It is surrounded by a concentric cylindrical tube of inner radius R2 and outer radius R3 as shown in the figure below, and it too carries a uniform charge density p. Determine the electric field as a function of the distance r from the center of the cylinders for R.
(1) Consider a very long uniformly charged cylinder with volume charge density p and radius R...
(1) Consider a very long uniformly charged cylinder with volume charge density p and radius R (we can consider the cylinder as infinitely long). Use Gauss's law to find the electric field produced inside and outside the cylinder. Check that the electric field that you calculate inside and outside the cylinder takes the same value at a distance R from the symmetry axis of the cylinder (on the surface of the cylinder) .
(20 pts) A thick, infinitely long cylinder, with radius R is uniformly charged with volume charge...
(20 pts) A thick, infinitely long cylinder, with radius R is uniformly charged with volume charge density p. Using Gauss's Law, find the electric field for (a) r < R, and (b) r > R. P R
A uniformly charged non-conducting sphere of radius a is placed at the center of a spherical...
A uniformly charged non-conducting sphere of radius a is placed at the center of a spherical conducting shell of inner radius b and outer radius c. A charge +Q is distributed uniformly throughout the inner sphere. The outer shell has charge -Q. Using Gauss' Law: a) Determine the electric field in the region r< a b) Determine the electric field in the region a < r < b c) Determine the electric field in the region r > c d)...
An infinitely long straight wire is uniformly charged with a positive linear charge density +?. It...
An infinitely long straight wire is uniformly charged with a
positive linear charge density +?. It is surrounded by an
insulating hollow cylinder (also infinitely long) of inner radius R
and outer radius 2R. The hollow cylinder has a uniform charge
density ?.
(a) Determine the value of ? if the electric field vanishes at
every point outside the cylinder (r > 2R).
(b) Determine the electric field in the region 0 < r <
R.
(c) Determine the electric...
Problem 8 A positive charge is uniformly distributed through an insulating sphere of radius R. The...
Problem 8 A positive charge is uniformly distributed through an insulating sphere of radius R. The point P that is located a distance r from the center of the sphere. (i) Determine the electric field when the point P is inside the sphere (r < R). (ii) Determine the electric field when the point P is outside the sphere (r > R). (iii) Plot the magnitude of the electric field as a function of r.
Consider an infinitely long cylinder of radius R with two spherical cavities, also of radius R....
Consider an infinitely long cylinder of radius R with two
spherical cavities, also of radius R. The cylinder carries a
uniform volume charge density of ρ. There are two point charges at
the center of the spherical cavities both of charge q.
Hint: Just as the previous hint, superposition is your friend. A
suggestion is to find the contributions from the cylinder and
spheres separately.
(a) Find the electric field at the points A, B, and C in the
diagram...
Problem 8 A positive charge is uniformly distributed through an insulating sphere of radius R. The...
Problem 8 A positive charge is uniformly distributed through an insulating sphere of radius R. The point P that is located a distance r from the center of the sphere. (i) Determine the electric field when the point P is inside the sphere (r < R). (i) Determine the electric field when the point P is outside the sphere (r> R). (iii) Plot the magnitude of the electric field as a function of r.
A charge, q, is uniformly distributed through a sphere of radius R. Surrounding the sphere is...
A charge, q, is uniformly distributed through a sphere of radius R. Surrounding the sphere is a conducting shell having inner radius 2R and outer radius 3R. The shell has a charge of -4q placed on it. a. What is the electric field and electric potential, relative to V = 0 at infinity at r for r > 3R? b. What is the electric field and electric potential at r for 3R > r > 2R? c. What is the...
A very long solid non-conducting cylinder of radius R1 is uniformly charged with a charge density p. It is surrounded by a concentric cylindrical tube of inner radius R2 and outer radius R3 as shown in the figure below, and it too carries a uniform charge density p. Determine the electric field as a function of the distance r from the center of the cylinders for R.
(20 pts) A thick, infinitely long cylinder, with radius R is uniformly charged with volume charge density p. Using Gauss's Law, find the electric field for (a) r < R, and (b) r > R. P R
An infinitely long straight wire is uniformly charged with a
positive linear charge density +?. It is surrounded by an
insulating hollow cylinder (also infinitely long) of inner radius R
and outer radius 2R. The hollow cylinder has a uniform charge
density ?.
(a) Determine the value of ? if the electric field vanishes at
every point outside the cylinder (r > 2R).
(b) Determine the electric field in the region 0 < r <
R.
(c) Determine the electric...
Problem 8 A positive charge is uniformly distributed through an insulating sphere of radius R. The point P that is located a distance r from the center of the sphere. (i) Determine the electric field when the point P is inside the sphere (r < R). (ii) Determine the electric field when the point P is outside the sphere (r > R). (iii) Plot the magnitude of the electric field as a function of r.
Consider an infinitely long cylinder of radius R with two
spherical cavities, also of radius R. The cylinder carries a
uniform volume charge density of ρ. There are two point charges at
the center of the spherical cavities both of charge q.
Hint: Just as the previous hint, superposition is your friend. A
suggestion is to find the contributions from the cylinder and
spheres separately.
(a) Find the electric field at the points A, B, and C in the
diagram...
Problem 8 A positive charge is uniformly distributed through an insulating sphere of radius R. The point P that is located a distance r from the center of the sphere. (i) Determine the electric field when the point P is inside the sphere (r < R). (i) Determine the electric field when the point P is outside the sphere (r> R). (iii) Plot the magnitude of the electric field as a function of r.
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