SP212
Worksheet 6
Ch 23.(3-6) Using Gauss’ Law
NOTE: Whenever we want to try and use Gauss’ law to find the electric field due to a a charge
distribution, we need to find some surface over which the magnitude of the electric field is constant.
This allows us to factor the electric field out of the flux integral.
SP212/3321&5521
Chapter 23 - Worksheet #2
Question 1: A hollow spherical conductor carries a net charge of Q=+2 µC. The hollow interior
Problem 1
of the sphere contains a point charge of q = 3 µC. (a) How much charge resides on the interior
surface of the conductor? (b) How much charge resides on the exterior surface of the conductor?
A spherical conductor has a spherical cavity carved out of the middle of it. The conductor carries a
(c) Suppose that the external radius of the conductor is R=0.35 m and that the charges on the
of +2
µC.itsInsurface
addition,
point surface
chargecharge
of size
−3 µC
has been
placed at the center of the
conductornet
are charge
spread evenly
across
(with aauniform
density
). What
is
the magnitude
of
the
electric
field
just
outside
the
conductor’s
exterior
surface?
(The
surface
area
cavity.
of a sphere is 4⇡R2 .) Does it point towards the sphere or away form it?
Q = +2 µC
q=
0.35 m
3 µC
a) What is the total charge that resides on the interior surface of the conductor?
HINT: Consider a spherical Gaussian surface that is just larger than the radius of the cavity.
b) What is the total charge that resides on the exterior surface of the conductor?
c) If the outer radius of the conductor is R = 0.35 m, what is the surface charge density on the outer
surface? What is the magnitude of the electric field just outside of the conductor near the outer
surface?(The surface area of a sphere is 4πR2 )
Problem 2
Question 2: Two very large conducting sheets are parallel and separated by a distance that is small
An infinitely long solid cylinder of radius R has a non-uniform
volume
~ = +2200 î N/C
in comparison to the size of either sheet. There is a uniform electric
field of E
2
withWhat
the isdistance
from
the
center
as inside
ρ = Ar
where
is aonconstant.
between them
the surface
charge
density
on the
surface
of theA
sheet
the right?
charge density that varies
E=2200
a) Consider a Gaussian surface that is a cylinder
of N/C
length L and radius r where r < R. What
is the total charge enclosed by this surface?
HINT: Think of the portion of the cylinder enclosed by the surface as a series of concentric infinitesimally thin cylindrical shells. How much charge is in each shell?
How would your answer change for r > R?
?
b) Using Gauss’ law and your results from part (a), what
is the electric field due to the cylinder of charge at a distance r where r < R?
HINT: In terms of the magnitude of the electric field E what is the electric flux through the Gaussian
surface (you only have to worry about the side of the surface, not the top or bottom).