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2) A long plastic cylinder with a radius of R and length L has a uniform...
A long cylinder or aluminum or radius R meters is charged so that it has a...
A long cylinder or aluminum or radius R meters is charged so that it has a uniform charge per unit length on its surface or (a) Find the electric fields at distances r (from the center of the cylinder) that lie inside and outside the cylinder. (Enter the radial component of the electric field. Use any variable or symbol stated above along with the following as necessary: inside outside E (b) Plot electric field magnitude as a function of distanoe...
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 charge is glued on the cylindrical surface of a long circular cylinder of radius R....
A charge
is glued on the cylindrical surface of a long circular cylinder of
radius R. The cylinder is made of a linear dielectric material of
dielectric constant
.
Find the electric field inside the cylinder and show that this
field is uniform.
If a small metal sphere of radius a (a<< R) gets into the
center of the cylinder, find the total dipole moment of the setup
by all charges: free charge, bound charge, and induced charge,
given the...
Consider an infinitely long straight cylinder of radius R and uniform positive charge density ρ. (a)...
Consider an infinitely long straight cylinder of radius R and uniform positive charge density ρ. (a) Find the field inside the cylinder a distance r < R from the center. (b) Find the field outside the cylinder a distance r > R from the center. (c) Sketch a plot of E vs r over the range 0 ≤ r ≤ 2R.
6. An infinite cylinder of radius R has a uniform charge density of p in its...
6. An infinite cylinder of radius R has a uniform charge density of p in its interior, and a surface charge density of -pR on its surface. Find the electric field everywhere inside and outside the cylinder. Be clear about both the magnitude and direction of the field.
Problem 3: the infinite cylinder An insulating cylinder that is infinitely long has radius R and...
Problem 3: the infinite cylinder An insulating cylinder that is infinitely long has radius R and a charge per unit length of λ. (Hint: because it is an insulator you should assume that the charge is spread uniformly across its entire volume of the cylinder) a) Use Gauss' Law to calculate the electric field at a point outside of the cylinder as a function of r, the radial distance from the center of the cylinder. (r> R) b) Use Gauss'...
Problem 5 Compute the total charge inside in a cylinder of length h and radius Rcy,...
Problem 5 Compute the total charge inside in a cylinder of length h and radius Rcy, when ρ(R) αR. Use the result to compute the electric field produced by the cylinder at points outside the cylinder (rRcyl). Note that since > Rcyl, the Gaussian surface (with radius r) encloses all the charge in the cylinder. State the direction of the electric field inside and outside the cylinder when a > 0, that is, when the cylinder carries positive charge. Problem...
Q5. FORCE DUE TO INDUCED POLARIZATION A) Consider a very long (effectively infinite) half-cylinder of radius...
Q5. FORCE DUE TO INDUCED POLARIZATION A) Consider a very long (effectively infinite) half-cylinder of radius r and uniform surface charge density o. What is the magnitude and direction of the electric field at the center of the cylinder? B) Consider now a thin, long straight wire with uniform positive charge per length 2 at the center of a half-cylinder of inner radius a and outer radius b. The half-cylinder is made of a linear dielectric with susceptibility Xe. You...
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...
The very long ( L 00) insulating cylinder has a uniform charge. Find the magnitude of...
The very long ( L 00) insulating cylinder has a uniform charge. Find the magnitude of the electric field as a function of in terms of the volume charge density p and radius R for both <T R and RCT Show that the two expressions agree on the boundary (r = R). L
A long cylinder or aluminum or radius R meters is charged so that it has a uniform charge per unit length on its surface or (a) Find the electric fields at distances r (from the center of the cylinder) that lie inside and outside the cylinder. (Enter the radial component of the electric field. Use any variable or symbol stated above along with the following as necessary: inside outside E (b) Plot electric field magnitude as a function of distanoe...
A charge
is glued on the cylindrical surface of a long circular cylinder of
radius R. The cylinder is made of a linear dielectric material of
dielectric constant
.
Find the electric field inside the cylinder and show that this
field is uniform.
If a small metal sphere of radius a (a<< R) gets into the
center of the cylinder, find the total dipole moment of the setup
by all charges: free charge, bound charge, and induced charge,
given the...
6. An infinite cylinder of radius R has a uniform charge density of p in its interior, and a surface charge density of -pR on its surface. Find the electric field everywhere inside and outside the cylinder. Be clear about both the magnitude and direction of the field.
Problem 3: the infinite cylinder An insulating cylinder that is infinitely long has radius R and a charge per unit length of λ. (Hint: because it is an insulator you should assume that the charge is spread uniformly across its entire volume of the cylinder) a) Use Gauss' Law to calculate the electric field at a point outside of the cylinder as a function of r, the radial distance from the center of the cylinder. (r> R) b) Use Gauss'...
Problem 5 Compute the total charge inside in a cylinder of length h and radius Rcy, when ρ(R) αR. Use the result to compute the electric field produced by the cylinder at points outside the cylinder (rRcyl). Note that since > Rcyl, the Gaussian surface (with radius r) encloses all the charge in the cylinder. State the direction of the electric field inside and outside the cylinder when a > 0, that is, when the cylinder carries positive charge. Problem...
Q5. FORCE DUE TO INDUCED POLARIZATION A) Consider a very long (effectively infinite) half-cylinder of radius r and uniform surface charge density o. What is the magnitude and direction of the electric field at the center of the cylinder? B) Consider now a thin, long straight wire with uniform positive charge per length 2 at the center of a half-cylinder of inner radius a and outer radius b. The half-cylinder is made of a linear dielectric with susceptibility Xe. You...
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...
The very long ( L 00) insulating cylinder has a uniform charge. Find the magnitude of the electric field as a function of in terms of the volume charge density p and radius R for both <T R and RCT Show that the two expressions agree on the boundary (r = R). L
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