Question

A circular cylinder with a radius R of 1 cm and a height H of 2 cm carries a charge density of pv = h R^2 uC/cm^3 (h is a point on the z-axis). The cylinder is then placed on the xy plane with its axis the same as the z-axis. Find the electric field intensity E and and the electric potential V on point A on z-axis 2 cm from the top of the cylinder.

Answer #1

10. A circular cylinder with a radius R of 1 cm and a
height H of 2 cm carries a charge density of ρV = H r2 sin φ µC/cm3
(r is a point on the z-axis, φ is an azimuthal angle). The cylinder
is then placed on the xy plane with its axis the same as the
z-axis. Find the electric field intensity E and the electric
potential V on point A on z-axis 2 cm from the top...

2. A circular ring with a radius R of 1 cm carries a charge
density of ?L = R sin ? (? is an azimuthal angle) µC/cm. The ring
is then placed on the xy plane with its axis the same as the
z-axis. Find the electric field intensity E and the electric
potential V on point A on z-axis 2 cm from the xy plane.

A circular ring of charge, with radius R,is placed in the
xy-plane and centered on the origin. The linear charge density of
the ring isλ=λ_o*cos^2(φ), where φ is the cylindrical polar
coordinate such that any point in space is indicated by (r, φ, z).
Find the electric potential anywhere on the z-axis as a function of
z . Using this electric potential find the electric field anywhere
on the z-axis also as a function of z

An infinitely long solid insulating cylinder of radius a = 2 cm
is positioned with its symmetry axis along the z-axis as shown. The
cylinder is uniformly charged with a charge density ρ = 27
μC/m3. Concentric with the cylinder is a cylindrical
conducting shell of inner radius b = 14.8 cm, and outer radius c =
17.8 cm. The conducting shell has a linear charge density λ =
-0.37μC/m.
1)
What is Ey(R), the y-component of the electric field...

Suppose the radius, height and volume of a right circular
cylinder are denoted as r, h, and V . The radius and height of this
cylinder are increasing as a function of time. If dr/dt = 2 and
dV/dt = 10π when r = 1, h = 2, what is the value of dh/dt at this
time?

A cylinder (bottom face at z= - L, top face at z = L, radius R,
centered along the z-axis) carries a volume charge distribution
?(?,?, ?) = ?o ( ?/ ? ) ???^2?.
a. Calculate the monopole and dipole moments of this charge
distribution
b. Find the leading order terms for the potential an the
electric field at the point (x = 25R, y = 25R, z = 25L)

An infinitely long solid insulating cylinder of radius a = 4.3
cm is positioned with its symmetry axis along the z-axis as shown.
The cylinder is uniformly charged with a charge density ρ = 29
μC/m3. Concentric with the cylinder is a cylindrical
conducting shell of inner radius b = 10.1 cm, and outer radius c =
12.1 cm. The conducting shell has a linear charge density λ =
-0.34μC/m.
What is V(P) – V(R), the potential difference between points...

A cylinder of radius R and height 2R is centered at the origin
of a coordinate system. The axis of the cylinder lies on the z
axis. The cylinder has a volume charge density given by p=
p0(1-z/R)*(sin ^2(phi)). Compute the quadruple moment. (Please
calculate all the components of Qij)

Charge is distributed uniformly throughout the volume of an
infinitely long cylinder of radius R = 12 cm. The volume charge
density ρ is 3.6 nC/m3. Find the magnitude of the electric field E
(a) inside the cylinder, a distance r = 6.6 cm from the cylinder
axis, and (b) outside the cylinder, a distance r = 24 cm from the
cylinder axis.

An infinitely long cylinder (radius R, centered along the
z-axis) carries a surface charge distribution σ(s = R,φ) = σ0
(4sinφ + 6cos2φ) . Using electricity and magnetism
a. Find expressions for the potential and electric field at
arbitrary points inside and outside the cylinder. b. Find the force
on a test charge 3q at the point (x = 3R, y = R, z = 4R), assuming
the test charge is too small to affect the potentials / fields
found...

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