29:28 Physics II
Spring 2005
First Hour Exam ...February 18, 2005

Write legibly. Start each question on a new page. It allows me to make comments and generally keeps me in a better mood. Clearly describe what you are trying to do; it can help for partial credit. There are 5 questions. Notice the table of fundamental constants attached to the exam. Good luck and no whining.

Walk with Ursus!!!

(1) Charge 1 is stuck (not free to move) and has a charge of $5 \mu C$ ( $1 \mu C = 10^{-6}$ Coulombs). Charge 2 is free to move and has a charge of $-3 \mu C$, and a mass of 30 grams (the mass of a portion of Wheaties). The charges are located 20 centimeters apart.
(a) What is the force between them? Be sure and say whether it is attractive or repulsive.
(b) Charge 2 is released from rest. It moves 10 cm from its original position. What is the distance between Charge 1 and Charge 2 now, and how fast is Charge 2 moving?

(2) A charge $q_1 = 5 \times 10^{-6}$ C is located at coordinates $(x,y,z)=(0,5,0)$ (distances in centimeters). A second charge $q_2= 3 \times 10^{-6}$ is located at $(x,y,z) = (0,-5,0)$. What is the vector electric field at a point $P$ with coordinates $(x,y,z) = (10,0,0)$ ?

(3) See Figure 1 below.
(a) What is the value of $\epsilon_0 \oint \vec{E} \cdot \vec{dA}$ for contour A (contour taken as the intersection of a closed surface with the plane of the paper)?
(b) What is the value of $\epsilon_0 \oint \vec{E} \cdot \vec{dA}$ for contour B?

Figure: Closed surfaces A and B surrounding charges

(4) A wire 4.0 m long and 6.0mm in diameter has a resistance of 15 m$\Omega$. A potential of 23 V is applied across the ends of the wire.
(a) What is the current in the wire?
(b) Calculate the resistivity of the wire material.

(5) A charged particle with charge $q$ (positive) and mass $m$ moves in one dimension (spatial coordinate $x$) in a potential given by

$$V(x) = V_0 \left( \sin(k\vert x\vert) -1 \right)$$ (1)

(a) Draw the potential energy of the particle as a function of $x$.
(b) Assume that the particle is released at $x=0$ with a speed

$$v = \sqrt \frac{2 q V_0}{3 m}$$ (2)

At what point (distance from the origin) will it be turned around?