A charge Q is distributed in the volume of a sphere of radius R
with a density non-uniform load cubic p = B (R - r) , where b is a
constant and r is the distance to the center of the sphere
determine: The values of the potential in the center and on the
surface of the sphere.
A nonconducting sphere of radius R carries a volume charge
density that is proportional to the distance from the center:
Rho=Ar for r<=R, where A is a constant; Rho = 0 for r>R
a) Find the total charge on the sphere
b) Find the electric field inside the charge distribution.
c) Find the electric field outside the charge distribution.
d) Sketch the graph of E versus r.
A sphere of radius R has a radius dependent charge density ρ = B
· r3 in terms of R and B.
Calculate the potential as a function of r from the center of
the sphere.
An isolated conducting sphere of radius R has charge
Q uniformly distributed on its surface. What is the
electric field (E) inside the conducting sphere at
distance r = R/2 from center?
Consider a conducting sphere of radius R carrying a net charge
Q.
a). Using Gauss’s law in integral form and the equation |E| =
σ/ε0 for conductors, nd the surface charge
density on the sphere. Does your answer match what you expect? b).
What is the electrostatic self energy of this sphere?
c). Assuming the sphere has a uniform density ρ, what is the
gravitational self energy of the sphere? (That is, what amount of
gravitational energy is required/released when...
A sphere of radius R is charged with a charge Q.
1. What is the potential outside of the sphere at distance r from
the center of the sphere?
2. what is the electric potential at the center of the
sphere
A solid insulating sphere of radius R has a charge of Q, (Q >
0) placed on it, uniformly distributed throughout its volume.
Surrounding the sphere is a spherical conducting shell with inner
radius 2R and outer radius 3R and has a charge of −2Q placed on it.
The sphere and the shell share the same center.
1A: Determine the magnitude of the electric field, E(r), where r
is the distance from the center of the sphere
1B: Determine the...
An insulating sphere of radius a has charge density
ρ(r) = ρ0r2, where
ρ0 is a constant with appropriate units. The
total charge on the sphere is -3q. Concentric with the
insulating sphere is a conducting spherical shell with inner radius
b > a and outer radius The total charge on
the shell is +2q. Determine
(a) The magnitude of electric field at the following
locations:
(i) r < a; ii) a < r < b; (iii) b
< r <...
A non conducting sphere of radius R and uniform volume charge
density is rotating with angular velocity, Omega. Assuming the
center of the sphere is at the origin of the coordinate system, a)
what is the magnitude and direction of the resulting magnetic field
on the z axis for any arbitrary z distance away from the origin
when z > R? b) same question as part a) but for z < R? Omega
of the rotating sphere on the extra...
A large sphere with radius R, supported near the earth's surface
as shown has charge density p(r) that varies as r^n (where n is
0,1,2..) for 0<r<R and reaches a max value of p as you get to
r=R. a non conducting uncharged string of length L with a second
tiny sphere of radius b, mass m, and excess charge q is suspended
from the large sphere as shown. suppose the string is cut gently
without otherwise disturbing the setup...