Use Gauss's Law to find the gravitational field g(r) and the
gravitational potential Phi(r) of an...
Use Gauss's Law to find the gravitational field g(r) and the
gravitational potential Phi(r) of an infinitely long cylinder on
the z-axis. (infty to -infty).
The cylinder has a constant mass density from (0 < r <
R).
*Use Gauss's Law: Q1. Find the electric field (outside and
inside) due to a uniformly charged solid sphere of radius “a” and
the total charge Q.
Explanation with drawing will be appreciated.
The gravitational potential is
U(r) = − GMsmp/r
d) r0 is the position of the minimum of the effective
potential. What does this signify for the planet’s trajectory?
e) Taylor expand out the effective potential about
r0. What is the period of oscillation for a small
perturbation about r0?
f) Show that the period of small oscillation about r0
is the same as the orbital period.
Use Ampere’s Law to determine the magnetic field as a function
of r (distance from the symmetry axis) both inside and outside an
infinitely long cylinder of radius R, carrying a current Iothat
is(show all relevant steps and any symmetry arguments in part a,
then you don’t have to repeat them in part b):
a) uniformly distributed over the surface of the cylinder (i.e.,
at r = R)
b) uniformly distributed throughout the cylinder
In a Gauss's Law problem where we use a cylinder for the
Gaussian surface, when we compute the surface we ignore the end
caps of the cylinder and just use 2*pi*r*L as an answer. Explain
why we drop out the geometry for the end caps.
6. Using Gauss’s Law, find the electric field a distance r from
a line of positive charge of infinite length and a constant charge
per unit length λ. Draw a diagram, a Gaussian surface and
completely prove your answer
Assume a planet with mass M and radius R.
(a) Find the strength of its gravitational field at the surface,
g. [5]
(b) Find the escape velocity, vesc, for a mass on the planet's
surface in terms of M and R. [10]
(c) Show that vesc=√2gR . [3]
(d) Calculate the numeric value of the escape velocity from
Earth without using Earth's mass. [2]
(a) Use Gauss’s Law for the electric field to show that the
electric field is discontinuous at the charged surface of a
conducting plane.
(b) Devise a way to apply this same approach to a patch on a
charged spherical conductor. Hint: Draw a diagram with the electric
field so you can specify the shape of the surface.
Write a short paragraph on what you understand by a force field.
Use gravitational and electric field concepts for your posting.
(ii) How is the concept of potential used in a force field?
Problem 2.
(a) Find the electric potential inside (r<R) and outside
(r>R) a uniformly charged solid sphere (with the charge density
roe) whose radius is R and whose total charge is Q. Use infinity as
your reference point. Plot schematically V(r) as a function of
r.
(b) [15%] By using the result for the electric potential in the
previous part, calculate the electric field in each region (r>R
and r<R)