Introductory Physics Volume Two

A Hints 181
2.27 Imagine that you build of the charge slowly. Suppose that you
have already got a charge q accumulated and you want to bring in an
amount dq more. How much work dW must you do? Once you have
dW written out you can integrate to get W .
2.28 Use Gauss’s law to find the field in all three regions. Then
integrate from infinity inward to find the electric potential. You will
need to split the integral into three regions because the form of the field
changes each time you cross the surface of a shell.
2.29 Look at the definition of capacitance.
2.30 Look at the definition of capacitance.
3.1 The amount of charge is equal to the number of particles times
the charge per particle.
3.2 You will need to use Ohm’s law, the definition of current density
and the relationship between the electric field and the electric potential
∆V = −E ∆x.
3.3 Use the result that R = ρL/A.
3.4 Use P = I ∆V .
3.5 Look up the theorem on electrical power.
3.6 Use the result of the example before this problem.
3.7 The current and voltage on the resistor can be negative (and they
are in this case).
3.8 Assume that the centripetal acceleration of the electron is caused
by the Coulomb force of the proton on the electron. Remember the
definition of electric current.
3.9 Remember that you know the charge of each electron, and that
current is the amount of charge per time.
3.10 Read the definition of current.
3.11 q = ∫ dq = ∫ dq
dt dt
3.12 First compute how many electrons pass a particular point in the
wire in one second. All of these electrons together fill a volume V of
the wire. From the number of electrons you can compute the volume of
electrons. Once you have the volume you can compute the length the
electrons occupy in the wire, since you know the cross sectional area
of the wire. But this length is the distance the electrons move in one
second.
3.13 Use the result that R = ρl/A.
3.14 Look up electric power.