A metal ball with diameter of a half a centimeter and hanging from an insulating thread is charged up with $1 \times 10^{10}$ excess electrons. An initially uncharged identical metal ball hanging from an insulating thread is brought in contact with the first ball, then moved away, and they hang so that the distance between their centers is 20 cm. Calculate the electric force one ball exerts on the other, and state whether it is attractive or repulsive. If you have to make any simplifying assumptions, state them explicitly and justify them.

A neutral solid metal sphere of radius 0.1 m is at the origin, polarized by a point charge of $6 \times 10^{-8}\ \mathrm{C}$ at location $\langle- 0.3,0,0\rangle\ \mathrm{m} .$ At location $\langle 0,0.07,0\rangle\ \mathrm{m},$ what is the electric field contributed by the polarization charges on the surface of the metal sphere? How do you know?

A metal ball with diameter of a half a centimeter and hanging from an insulating thread is charged up with $1 \times 10^{10}$ excess electrons. An initially uncharged identical metal ball hanging from an insulating thread is brought in contact with the first ball, then moved away, and they hang so that the distance between their centers is 20 cm. Now the balls are moved so that as they hang, the distance between their centers is only 5 cm. Naively one would expect the force that one ball exerts on the other to increase by a factor of $4^{2}=16,$ but in real life the increase is a bit less than a factor of 16. Explain why, including a diagram. (Nothing but the distance between centers is changed-the charge on each ball is unchanged, and no other objects are around.)

What are some positive teamworking behaviors you practice?

Which of the following are true? Check all that apply. (1) If the net electric field at a particular location inside a piece of metal is zero, the metal is not in equilibrium. (2) The net electric field inside a block of metal is zero under all circumstances. (3) The net electric field at any location inside a block of copper is zero if the copper block is in equilibrium. (4) The electric field from an external charge cannot penetrate to the center of a block of iron. (5) In equilibrium, there is a net flow of mobile charged particles inside a conductor.

How did World War II change the ethnic diversity of Poland?

The following data represent the cost C (in thousands of dollars) of manufacturing Chevy Cobalts and the number x of Cobalts produced. Draw a scatter diagram of the data using x as the independent variable and C as the dependent variable. Comment on the type of relation that may exist between the two variables C and x.

$$\begin{matrix} \text{Number of Cobalts} & \text{Cost, C}\\ \text{Produced, x} & \text{ }\\ \text{0} & \text{10}\\ \text{1} & \text{23}\\ \text{2} & \text{31}\\ \text{3} & \text{38}\\ \text{4} & \text{43}\\ \text{5} & \text{50}\\ \text{6} & \text{59}\\ \text{7} & \text{70}\\ \text{8} & \text{85}\\ \text{9} & \text{105}\\ \text{10} & \text{135}\\ \end{matrix}$$

Determine whether each statement is true or false. If the statement is true, prove it. If the statement is false, give a counterexample. Assume that the functions $f$, $g$, and $h$ take on only positive values.

$$(2n)^2=\Omega(n^2)$$

Find the slope of the line that passes through the points. (-3, -2) and (-3, 6)

En sus pinturas, Antonio Berni representa un deporte en particular. ¿Cuál es?

Which of the following are true? Select all that apply. (1) In equilibrium, there is no net flow of mobile charged particles inside a conductor. (2) The electric field from an external charge cannot penetrate to the center of a block of iron. (3) The net electric field inside a block of aluminum is zero under all circumstances. (4) If the net electric field at a particular location inside a piece of metal is not zero, the metal is not in equilibrium. (5) The net electric field at any location inside a block of copper is zero if the copper block is in equilibrium.

The functions f and g are defined by

$$\begin{array}{l}{f(x)=\frac{4}{x}, x \in \mathbb{R}, x \neq 0} \\ {g(x)=2 x, x \in \mathbb{R}}\end{array}$$

a. Sketch the graph of f(x) for $-8 \leq x \leq 8$. b. Write down the equations of the horizontal and vertical asymptotes of the function f. c. Sketch the graph of g on the same axes. d. Find the solutions of $\frac{4}{x}=2 x$. e. Write down the range of function f.

Four point particles are located at the corners of a square (shown in the given figure). The two particles on the left each carry a charge $+Q$. If the electric field at the center of the square is directed to the right (along the $+x$ axis), what might the charges on the particles on the right be?

Consider the VPython program shown below. An important skill is being able to read and understand an existing program, in order to be able to make useful modifications. Before running the program, study the program carefully line by line, then answer the following questions: (1) What is the initial velocity of the particle? (2) Is the particle initially located in front of the box or behind it? (3) In which line of code is the position of the particle updated? (4) What is the value of the time step $\Delta t?$ (5) Will the particle bounce off of the red box, or travel through it?

$$\begin{array}{l}{\text { from visual import } *} \\ {\text { box }(\text { pos }=\text { vector }(0,0,-1),} \\ {\operatorname{size}=(5,5,0.5)} \\ {\text { color }=\operatorname{colos} . \text { red }} \\ {\text { opacity }=0.4 \text { ) }} \\ \text { particle }=\text { sphere (pos=vector }(-5,0,-5), \\ {\text { radius }=0.3,} \\ {\text { color }=\mathrm{color} \text { . cyan, }} \\ {\left.\text { make }_{-} \text {trail }=\text { True }\right)}\\ {v=\operatorname{vector}(0.5,0,0.5)} \\ {\operatorname{delta}_{-} t=0.05} \\ {t=0} \\ {\text { while } t<20 :}\end{array} \\ {\text { rate }(100)} \\ \text { part icle. pos }=\text { part icle. pos }+\mathrm{v}^{*} \text { delta}_{-} \mathrm{t}\\ t=t+\operatorname{delta}_{-} \mathrm{t}$$