MT2—A
Activity ID:
1. In a series LRC circuit the magnitude of the phase angle is ' = 54.0 , with the source voltage lagging the
current. Assume C = 2.5 µF, R = 180 ⌦, f = 200 Hz, and the average power delivered by the source is Pavg =
140 W.
(a) What is the inductance in this circuit?
(b) What is the rms current in this circuit?
(c) What is the rms voltage of the source?
(d) What is the average power dissipated if the frequency is changed to the resonant frequency?
2
Activity ID:
2. Crystalline solids have their atoms arranged in highly symmetric arrays called lattices. The triangular lattice
structure of a particular solid is shown in the diagram below: there are six positive charges +q arranged in a
hexagon with side length d and the solid is doped with an atom carrying a charge Q at the middle site. Assume
Q has mass M and is confined to move along the z-axis. You can ignore the force of gravity.
(a) What is the magnitude and direction of the net force F~ on Q as a function of z?
(b) What is the magnitude of F~ when |z|
d?
(c) What is the magnitude of F~ when |z| ⌧ d?
(d) In real solids only |z| ⌧ d makes sense and the force on Q obeys a Hook’s law type relation, Fz = Kz.
What is the spring constant K in terms of the parameters given?
(e) [Bonus] What is the period of oscillation of Q?
z
Top view
–Q
+q
+q
+q
+q
+q
d
+q
d
3
Activity ID:
3. A very long, insulating cylinder with radius R has a cylindrical hole of radius R/2 bored along its entire length
(see figure). The axis of the hole is a distance R/2 from the axis of the cylinder. The solid material of the cylinder
has a uniform positive charge density ⇢.
~ A at the point A = (3R/4, R/4) inside the hole?
(a) What is the magnitude and direction of the electric field E
Express your answer in terms of ⇢, R, and ✏0 .
~ vary with distance from the center axis?
(b) Sketch the electric field at all points inside the hole. How does E
~
(c) What is the electric field EB at the point B = (0, R) at the top of the cylinder?
B
A
R
O
R/2
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