An infinitely long solid insulating cylinder of radius a = 2.2 cm is positioned with its symmetry axis along the z-axis as shown. The cylinder is uniformly charged with a charge density ρ = 48 μC/m3. Concentric with the cylinder is a cylindrical conducting shell of inner radius b = 18.3 cm, and outer radius C =20.3 cm. The conducting shell has a linear charge density λ = 0.56 μC/m3.
An infinitely long solid insulating cylinder of radius a = 2.1
cm is positioned with its symmetry axis along the z-axis as shown.
The cylinder is uniformly charged with a charge density ρ = 27μC/m3. Concentric with the cylinder is a cylindrical
conducting shell of inner radius b = 14.9 cm, and outer radius c =
17.9 cm. The conducting shell has a linear charge density λ =
-0.36μC/m.1 What is Ey(R), the y-component of the electric
field at point...
An infinitely long solid insulating cylinder of radius a = 2.1
cm is positioned with its symmetry axis along the z-axis as shown.
The cylinder is uniformly charged with a charge density ρ = 27μC/m3. Concentric with the cylinder is a cylindrical
conducting shell of inner radius b = 14.9 cm, and outer radius c =
17.9 cm. The conducting shell has a linear charge density λ =
-0.36μC/m.1 What is Ey(R), the y-component of the electric
field at point...
An infinitely long solid insulating cylinder of radius a = 5.6
cm is positioned with its symmetry axis along the z-axis as shown.
The cylinder is uniformly charged with a charge density ρ = 25
μC/m3. Concentric with the cylinder is a cylindrical
conducting shell of inner radius b = 14.5 cm, and outer radius c =
17.5 cm. The conducting shell has a linear charge density λ =
-0.41μC/m.
1. What is V(P) – V(R), the potential difference between...
An infinitely long solid insulating cylinder of radius a = 4.4
cm is positioned with its symmetry axis along the z-axis as shown.
The cylinder is uniformly charged with a charge density p = 29
uC/m^3. Concentric with the cylinder is cylindrical conduction
shell of inner radius b = 10.2cm and outer radius c= 12.2 cm. The
conducting shell has a linear charge density = -0.33 uC/m.
1. What is Ey (R), the y-component of the electric field at
point...
An infinitely long solid insulating cylinder of radius a = 5.6
cm is positioned with its symmetry axis along the z-axis as shown.
The cylinder is uniformly charged with a charge density ρ = 45
μC/m3. Concentric with the cylinder is a cylindrical
conducting shell of inner radius b = 17.9 cm, and outer radius c =
19.9 cm. The conducting shell has a linear charge density λ =
-0.31μC/m.
1)
What is Ey(R), the y-component of the electric field...
1. An infinitely long non-conducting right-circular cylinder of
radius a, oriented concentrically with the z-axis, carries uniform
charge density ?0. It is surrounded concentrically by an infinite
long grounded right-circular conducting cylindrical shell of inner
radius b and outer radius c. Ground potential is zero.
(a) (4 points) What is the linear charge density (charge per unit
length) ? of the inner nonconducting cylinder.
(b) (4 points) What are the linear charge densities (charge per
unit length) ? on the...
Use the separation of variables method to solve the following
problem. Consider a long, narrow
tube connecting two large, well-mixed reservoirs containing a
small concentration of N2 in another
inert gas. The tube length is L = 100 cm. To establish an
initial concentration profile in the
tube, each reservoir is held at a fixed concentration:
Reservoir 1 contains no N2 and reservoir 2 has
2 × 10−6 mol/cm3 of N2.
(a) At t = 0, the concentrations of the...
An infinitely long right circular cylinder has radius ?. There
is a non-constant cylindrically symmetric volume charge density
?(?), where ? is the (radial) distance from the axis of the
cylinder, given by ?(?) = ((?0*?)/?)sin((2??)/?), where ?0 is a
constant.
1. Consider a concentric cylinder with radius ? and length ?.
Compute the total charge ?(?) inside the cylinder for 0 < ? <
? and for ? > ?.
2. Go back to the infinite cylinder setup and...
An infinitely long hollow cylinder of radius R is carrying a
uniform surface charge density σ (φ).
(a) Determine the general form of the solution of Laplace’s
equation for this geometry.
(b) Use the boundary condition σ(φ) = σ0cos(φ) to determine
the potential inside and outside of the cylinder.
(c) Using your answer to part (b), determine the electric
field inside and outside of the cylinder.