Download PHY 113, Summer 2007

PHY 114, Summer 2007
Langenbrunner
HW 7 – due Tuesday, July 31 in class
1. Given a 7.4 pF air-filled capacitor, you are asked to convert it to a capacitor that can store up
to 7.4 J with a maximum potential difference of 652 V. What is the dielectric constant of the
dielectric you need to use to fill the gap in the capacitor?
2. Two parallel plates of area 100 cm2 are given charges of equal magnitudes 8.9 x 10-7 C but
opposite signs. The electric field within the dielectric material filling the space between the
plates is 1.4 x 106 V/m. Calculate the dielectric constant of the material.
3. At a given instant the current and self-induced emf in an inductor are directed as shown in the
figure below.
i
-
+
a) Is the current increasing or decreasing?
b) The induced emf is 17 V and the rate of change of the current is 25 kA/s; find the inductance.
4. A circular loop of wire 50 mm in radius carries a current of 100 A.
a) Find the magnetic field strength at the center of the loop.
b) Calculate the energy density at the center of the loop.
5. Two solenoids are part of the spark coil of an automobile. When the current in coil 2
increases at the rate 15.0 A/s, the emf in coil 1 is 25.0 mV.
a) What is their mutual inductance?
b) When coil 1 has current of 3.60 A, what is the flux through coil 2?
6. A solenoid wrapped around a diamond core is 26 cm long, 1 cm in radius, and has 380 turns.
The magnetic susceptibility for diamond is -2.2 x 10-5. (Assume that the diamond core fills the
solenoid entirely.)
a) When a current of 5A flows through the wire, what is the magnetic field strength inside the
solenoid?
b) Does the diamond core affect the inductance of this solenoid? How? (Be specific.)
7. An inductor holds 5 J of stored energy for every 1A of current running through it.
a) What is the inductance L of this inductor?
b) Show that you get the correct units for part a), if you didn't already.
8. A dielectric is pulled from between the plates of a capacitor while the capacitor remains
connected to a battery. Describe the changes that occur to the potential difference of the
capacitor, the charge stored, the capacitance, the energy stored, and the electric field between the
plates. Explain your answers.
9. A dielectric is pulled from between the plates of a capacitor after the capacitor is disconnected
from the battery. Give one example of a difference between this situation and the one described
in #8.
10. A rectangular loop of N close-packed turns is positioned near a long straight wire as shown in
the figure below.
a) Find the net flux through the loop due to the wire, in terms of the current i.
b) What is the mutual inductance M for the loop-wire combination?
c) Evaluate M for N=100, a=1.0 cm, b=8.0 cm, and c=30 cm.
i
a
b
c
11. Review the wave equation material that you learned about in 113 (or whatever your
Mechanics class was), with an eye toward the wave equations we got from the differential form
of Maxwell's equations in class. You'll see a lot of them on Monday.