Question

isolated spherical shell with radius f R which is under uniform electric field a long thw z axis. what is the electric dipole moment of the sphere.

Answer #1

A perfectly conducting sphere with radius a is placed in a
uniform electric field Eo
(a) What is the surface charge density on the sphere?
(b) What is the induced dipole moment of the sphere?

Electric Field of a Charged Sphere with a small hole on the
surface.
Consider a spherical shell of radius R centered on the origin of
coordinates. The sphere is uniformly charged, with total charge Q,
except for the region where theta <= 1.00?. Consider field point
on the positive z-axis. Determine E as a function of z.

Answer with a drawing please!
A nonconducting spherical shell of inner radius R1 and
outer radius R2 contains a uniform volume charge density
ρ throughout the shell. Derive he magnitude of the
electric field at the
following radial distances r from the center of the
sphere:
a) r<R1
b) R1<r<R2
c) r>R2

A thin spherical shell has a radius a and charge +Q that is
distributed uniformly overr it. There is also a second spherical
shell of radius b that is concentric with the first shell and has
charge +Q2 uniformly distributed over it. b> a. Find the
magnitude and direction of electric field in the regions (a) R<a
(b)a<R<b (c)R>b (d) electric potential for the region
R>b (e) electric potential for the region a<R<b
(f)electric potential for the region R<a

The figure shows a spherical shell with uniform volume charge
density ρ = 2.17 nC/m3, inner radius a
= 10.4 cm, and outer radius b = 3.0a. What is the
magnitude of the electric field at radial distances
(a) r = 0; (b)
r = a/2.00, (c) r =
a, (d) r = 1.50a,
(e) r = b, and
(f) r = 3.00b?

Charge is distributed throughout a spherical shell of inner
radius r1 and outer radius r2 with a volume density given by ρ = ρ0
r1/r, where ρ0 is a constant. Determine the electric field due to
this charge as a function of r, the distance from the center of the
shell.
In this problem the volume charge density ρ is not uniform; it
is a function of r (distance from the center.)

Show, by integrating Coulomb’s Law, that the field anywhere
inside of a spherical shell with uniform surface-charge
distribution, is zero. You are not allowed to make use of Gauss’
Theorem. Hint: start by showing that the field anywhere along an
axis of the sphere is zero. Then, reason that any point within the
sphere can be considered to be along a symmetry axis. Warning:
be careful, once you do the integral, to make sure you take
consistent signs for square...

Show, by integrating Coulomb’s Law, that the field anywhere
inside of a spherical shell with uniform surface-charge
distribution, is zero. You are not allowed to make use of Gauss’
Theorem. Hint: start by showing that the field anywhere along an
axis of the sphere is zero. Then, reason that any point within the
sphere can be considered to be along a symmetry axis. Warning:
be careful, once you do the integral, to make sure you take
consistent signs for square...

A uniform spherical shell of mass M = 3.2 kg and radius
R = 7.8 cm can rotate about a vertical axis on
frictionless bearings (see figure below). A massless cord passes
around the equator of the shell, over a pulley of rotational
inertia I = 3.0 ? 10?3 kg · m2 and
radius r = 5.0 cm, and is attached to a small object of
mass m = 0.60 kg. There is no friction on the pulley's
axle; the...

A uniform spherical shell of mass M = 17.0 kg and radius R =
0.310 m can rotate about a vertical axis on frictionless bearings
(see the figure). A massless cord passes around the equator of the
shell, over a pulley of rotational inertia I = 0.210 kg·m2 and
radius r = 0.100 m, and is attached to a small object of mass m =
1.50 kg. There is no friction on the pulley's axle; the cord does
not slip...

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