Name:
Honors General Physics II - HW 2 - Due Wednesday, Sep. 17
Problem 1
What is the vertical component of the electric field acting on a test charge q0 at the center
a half-ring of charge q, radius a, and uniform charge density λ = q/(πa)?
Ey
q0
1
Name:
Honors General Physics II - HW 2 - Due Wednesday, Sep. 17
Problem 2
Not graded. Extra practice.
A solid sphere of charge q and radius a, is surrounded by a cloud of charges.
The cloud’s charge density falls of with the distance as ρ = β/r, where β is a constant.
ρ
a
a) What is the net external electric field at some distance r > a?
b) There is a peculiar amount of charge q that the sphere can have to cause the net
external field to be independent on the distance r. What is it?
2
Name:
Honors General Physics II - HW 2 - Due Wednesday, Sep. 17
Problem 3
What is the capacitance of two hollow, concentric spherical metal surfaces?
The inner and outer radii are a and b and the inner and outer charges are Q and −Q.
b
a
3
Name:
Honors General Physics II - HW 2 - Due Wednesday, Sep. 17
Problem 4
A sphere of radius a has charge Q uniformly distributed throughout the interior.
a) Use Gauss’s Law to find the electric field strength inside and outside the sphere.
b) The energy density of a region of space with a radial electric field is u(r) = (ϵ0 /2)E(r)2 .
Use this to figure out the potential energy stored inside and outside the sphere.
Think of the differential volume dV as skins of an onion of area 4πr2 and thickness dr.
c) Show that the internal potential energy is a fifth of the external potential energy.
4
Name:
Honors General Physics II - HW 2 - Due Wednesday, Sep. 17
Problem 5
x=0
x=L
V
−
+
The cylindrical part of the diagram is a zoomed in part of a wire between x = 0 and x = L.
This segment of the wire has a cross-sectional area A.
a) What is the resistance R of this wire segment if it has a constant resistivity ρ = ρ0 ?
b) Now, assume that this wire segment has a resistivity which increases linearly with distance; ρ(x) = (ρ0 /L) x, where ρ0 and L are constants and x is some distance between
x = 0 and x = L.
Calculate the equivalent resistance between x = 0 and x = L.
Hint: Split the segment up into infinitesimally short pieces of length dx in “series”.
5
Name:
Honors General Physics II - HW 2 - Due Wednesday, Sep. 17
Problem 6
R
I3
I1
R
+
−
−
V
+
I2
V
R
R
a) How are the currents related at the top junction?
b) Write down the potential tallies for the left and right loops.
c) For this and the next part, take V = 5 [V] and R = 1 [Ω]. Solve for the three currents.
d) Find the magnitude of the potential across the gray resistor.
6
0
