Question

Assuming that the gravitational acceleration inside a homogeneous spherical shell is zero, show that the gravitational acceleration inside a homogenous uniform solid sphere is proportional to the distance from its center.

Answer #1

A uniform solid sphere of radius R = 3.6 km produces a
gravitational acceleration of ag on its surface. At what distance
from the sphere's center are there points (a) inside and (b)
outside the sphere where the gravitational acceleration is
ag/8?

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 Charged Spherical Shell and a Point Charge.
A spherical conducting shell of radius 1.21 [m], carries charge
4.10×10-6 [C], distributed uniformly over its surface.
At the center of the shell there is a point charge
3.90×10-9 [C].
Let Pi and Po be points inside and outside
the spherical shell, respectively. The distance of Pi
from the point charge is 1.06 [m], whereas is Po is 5.27
[m] away from the point charge.
Calculate the electrostatic potential at a Pi...

1) A spherical shell with a radius of 0.500 m is uniformly
charged and generates an electric field. The field has a strength
of 7.50 N/C at a distance of 1.00 m from the center of the sphere.
(a) What is the strength of the field 2.00 m from the center of the
sphere? (b) What is the strength of the field 10.0 m from the
center of the sphere? (c) What is the strength of the field inside
the...

A uniform solid sphere of mass m1 and radius R1 is inside and
concentric with a spherical shell of mass m2 and radius R2. Find
the gravitational force exerted by spheres on a particle of mass m
located at (1).r < R1 (2).R1 < r < R2 (3).r > R2

A point charge + 5.0 ?C is at the center of an electrically
neutral spherical shell with a radius of 12.0 cm. (i) What
is the total electric flux about the sphere shell? (ii) What is
the magnitude of the electric field at a distance 0.30 m from
the center?

A thin spherical shell with radius R1 = 4.00cm is
concentric with a larger thin spherical shell with radius 7.00cm .
Both shells are made of insulating material. The smaller shell has
charge q1=+6.00nC distributed uniformly over its surface,
and the larger shell has charge q2=?9.00nC distributed
uniformly over its surface. Take the electric potential to be zero
at an infinite distance from both shells.
Part A
What is the electric potential due to the two shells at the
following...

Consider two concentric spherical shells with different radii,
namely one is inside the other. The spherical shell inside has
radius R1 = 7.00 cm and charge q1 = +3.00×10^-6 C; the spherical
shell outside has radius R2 = 17.0 cm and charge q2 = −5.00×10^-6
C. For both shells charges are distributed uniformly over their
surfaces. Assume that V = 0 at large distances from both
shells.
A) Find the electric potential of the two shells at the distance r...

. Calculate the potential energy stored in a spherical shell
uniformly charged with full charge q and radius R. Show that the
two expressions of the energy (depending on the potential and the
field) give the same result.
a. If we now fill this one with the same material, in order to
make it a solid sphere of the same size, and maintain the same
amount of charge, what is its energy?
b. compare the energy of the two configurations,...

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