Introductory Physics Volume Two

A Hints 179
1.14 Since this is only an estimate, assume that you are composed
entirely of water.
1.16 Be sure to add the parts as vectors.
1.17 Let the charge elements dq be little sections of arc that subtend
and angle dθ. Notice that the full charge is spread over a half a circle
so that the charge density (charge per angle) is −7.5µC
π
, so that dq =
−7.5µC
π
dθ.
1.18 Use the work energy theorem. Recall that work is force time
distance.
1.19 This is like a projectile motion problem, but this time we have
a constant electric force rather than an constant gravitational force.
1.20 Start by making a free body diagram and be sure to include the
force of gravity and the force of the string.
1.21 A flux is negative if it is into the volume of the box and positive
if the flux is out of the volume of the box.
1.22 There is a very easy way to do this problem, by using the fact
that there is no charge inside the volume of the nose cone.
1.25 ⃗r = −xî
2.1 Look at the definition of electric potential, how is the electric
potential related to potential energy?
2.2 Use the work energy theorem.
2.3 Follow the example in the text for a nonuniform field.
2.4 Follow the example in the text.
2.6 Consider a closed surface that is totally within the outer conductor
and surrounds the inside surface of the outer conductor, as indicated
by the dotted line in the figure. Using the fact that there is no field
inside a conductor argue that the electric flux through this surface is
zero. From this use Gauss’s law to find the charge on the inside surface
of the outer conductor. Next use the fact that the total charge on the
outer conductor is equal to the sum of the charge on its two surfaces,
to find the charge on the outside surface of the outer conductor.
2.7 Use Gauss’s law. Remember that the electric field is zero inside
the body of a conductor.
2.8 Use the definition of capacitance.
2.9 Use the fact that the electric field strength between the plates is
both σ/ɛ 0 and ∆V/d, where σ is the charge density on the plates.
2.10 Assume that the capacitor is charged so that the inside sphere
has a charge Q and the outside sphere has a charge −Q. Use Gauss’s
law to get the field strength between the shells.