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Physics 112 HW6
/6
DUE Wednesday, 17 September 2014
U2-GL01. Two concentric conducting shells have a point charge +q right
in the middle as shown in the diagram at right (the grey color indicates
the “meat” of each conductor). The inner shell has a total charge of -2q,
but the outer shell is neutral. The point charge does not touch the
conductors. Find expressions for the electric field in all regions (r<a,
a<r<b, etc.) and the net charge on each surface of each shell. Your
expressions may contain the terms q, r, and fundamental constants.
-2q
U2-GL02. (Wolfson, Ch. 21 Problem 51) An infinitely thin spherical shell 30
cm in diameter carries a total charge of 85 μC distributed uniformly over its
surface. A 1.0 μC point charge is located at the center of the shell. What is
the electric field strength (a) 5.0 cm from the center and (b) 45 cm from the
center? (c) How would your answers change if the charge on the shell were
doubled?
b
a
+q
c
d
85 μC
30 cm
1 μC
U2-GL03. (Wolfson, Ch. 21 Problem 52) A thick, spherical shell of inner radius
a and outer radius b carries a uniform volume charge density ρ. Find expressions for the electric field
in the regions r < a, a < r < b, and r > b.
U2-GL05. (Wolfson, Ch. 21 Problem 61) An irregular conductor carries a net
charge Q. It also has an irregular, empty cavity.
a) Show that the electric field inside the cavity must be zero.
b) If you put a point charge inside the cavity, what value must it have in order
to make the surface charge density on the outer surface of the conductor
everywhere zero?
U2-GLS-01. A spherical region of space of radius R contains a spherically symmetric charge density
𝐶
given by 𝜌(𝑟 ≤ 𝑅) = , where C is a constant with units of Coulombs per meters2.
𝑟
a) Determine an expression for the total amount of charge in this region in terms of C, R, and
fundamental constants.
b) Determine an expression for the electric field for r < R in terms of C, r, and fundamental constants.
“Blanchard’s Charge” A metallic ball carrying charge q is
introduced into a conducting shell within a conducting shell.
It is touched to the interior of the inner conducting shell, and
then withdrawn. Note that both shells have a hole at their top,
as shown in the diagram.
a) What is the final charge of the ball?
b) Explain how much charge is left where on the
conducting shells.
c) Repeat parts a) and b) if the ball is inserted between the
inner and outer conductors and touched to the inside of
the outer conductor.
+q
Insulating
supports