Name:

PHYSICS 232
Midterm 1, February 27 , 1998, 5:30pm-6:45pm
Instructor: P. Q. Hung

25 points for each problem. READ the problems carefully. SHOW YOUR WORK. DO NOT JUST write the answers down and *PLEASE* DO NOT SCRIBBLE. ANSWERS WITHOUT EXPLANATION WILL BE GIVEN NO CREDIT. CIRCLE YOUR ANSWERS!

Useful formulas (not necessarily applied to all problems below):

$\vec{F} = m\vec{a}$

$x = x_{0} + v_{0x} t + \frac{1}{2} a_{x} t^2$

$y = y_{0} + v_{0y} t + \frac{1}{2} a_{y} t^2$

$F = k \frac{q_{1} q_{2}}{r^2}$

$\vec{E} = k \frac{q}{r^2} \hat{r}$

$Q = \int \rho dV$. For $\rho = \rho (r)$,

$V= k \frac{q}{r}$

$V_B - V_A = -\int_{A}^{B} \vec{E} \cdot d\vec{s}$

$\Phi = \oint \vec{E} \cdot d\vec{A} = 4 \pi k Q$

$C= \frac{Q}{V}$

$E = \frac{\sigma}{\epsilon_0}$

$C = \epsilon_0 \frac{A}{d}$

$I = \frac{dQ}{dt}$, V= I R

$U = \frac{1}{2} Q V = \frac{1}{2} C V^2$

I = nqv_d A

P= I²R = V²/R

$k = 8.99 \times 10^9 N\cdot m^2/C^2$

$\epsilon_0 = 1/4\pi k = 8.85 \times 10^{-12} C^2/N\cdot m^2$

$e= 1.6 \times 10^{-19} C$

$\int x^n dx = \frac{x^{n+1}}{n+1}$

1) An object having a mass of 10.0 g and a charge of $+8.00 \times 10^{-5}$ C is placed in an electric field $\vec{E} = 3.00 \times 10^{3} \frac{N}{C} \hat{\imath} - 600 \frac{N}{C} \hat{\jmath}$.(a) What are the magnitude and direction of the force on the object? (15pts) For the direction, please give the angle that the force makes with respect to the positive x axis. (b) If the object is released from rest at the origin, what will be its coordinates after 3.00 s? (10pts)

2) A solid nonconducting sphere of radius R has a charge distribution of volume charge density $\rho = \rho_{s} \frac{r}{R}$,where $\rho_{s}$ is a constant and r is the distance from the center of the sphere. (a) What is the total charge Q of the sphere? (8pts) (b) What is the magnitude of the electric field inside the sphere and at a distance r from the center of the sphere? Express your answer in terms of Q instead of $\rho_{s}$. (17pts)

3) A point charge q₁ = +6.0 e is fixed at the origin of a rectangular coordinate system, and a second point charge q₂ = -10 e is fixed at x= 8.6 nm, y=0. The locus of all points in the xy plane with V=0 (other than at infinity) is a circle centered on the x-axis, as shown in the Figure below. Find (a) the location x_c of the center of the circle (12.5pts) and (b) the radius R of the circle (12.5pts). Hint: Find two points on the circle that can facilitate your computation. There should be two equations with two unknowns. You will not have to solve any quadratic equation.

4) In the Figure below, find the equivalent resistance between points (a) F and H (12.5pts) and (b) F and G (12.5 pts). Hint: For each pair of points, imagine that a battery is connected across the pair.