Introductory Physics Volume Two

1.7 More Examples 23
⊲ Problem 1.11
Consider a long cylindrical charge distribution of radius R with a uniform
charge density ρ. Find the electric field at a distance r from the
axis for r < R.
⊲ Problem 1.12
A spherical shell of radius R carries a net charge of Q uniformly distributed
over it’s surface.
(a) Find the electric field strength at a point inside the shell.
(b) Find the electric field strength at a point outside the shell.
§ 1.7 More Examples
Example
Return to the pithballs in the example in section 1: assume the length
of each string is 10cm. If the masses have the same net electric charge,
what is the magnitude of the charge on each mass? Can you determine
the sign of the net charge on each ball?
Use the following diagram to determine the distances between the
masses:
L
θ/2
L = 10cm
d
d = 2L sin θ 2 = 2(10cm) sin 5◦ = 1.7cm.
Assume each mass has a charge q, then using Coulomb’s law:
F E = 1 q 2
4πɛ 0 d 2 −→ q2 = F Ed 2
1
4πɛ 0
.
√
(0.0034N)(.017m)
−→ q =
2
9 × 10 9 N · m 2 /C 2 = 1.0 × 10−8 C
The sign of the charge cannot be determined; all that can be said is
the net charge on the masses have the same sign.
Example
Three particles with electric charge are attached to a meter stick, as
shown. The value of Q is 1 × 10 −6 C (= 1µC). (a) What is the electric
force on the center charge? (b) To what position could the center charge
be moved so that the net electric force on it is zero?