A student was given the following problem: A 0.20-kg cannonball with a $+1.0 \times 10^{-4} \mathrm{C}$ charge starts at rest 0.40 m from a fixed $+2.0 \times 10^{-4} \mathrm{C}$ charge. When the cannonball is released, it flies vertically upward.How fast is it moving when 10 m above the fixed charge? The student gave this solution:

$$\begin{array}{l}{\left(9.0 \times 10^{9} \mathrm{Nm}^{2} / \mathrm{C}^{2}\right)\left(+2.0 \times 10^{-4} \mathrm{C}\right)\left(+1.0 \times 10^{-4} \mathrm{C}\right) /(0.40 \mathrm{m})^{2}} \\ {=(1 / 2)(10 \mathrm{kg}) v_{y}^{2}+(0.20 \mathrm{kg})\left(9.8 \mathrm{m} / \mathrm{s}^{2}\right)(10 \mathrm{m})}\end{array}$$

or $v_{y}=15 \mathrm{m} / \mathrm{s}$. Evaluate the solution to this problem and correct any errors you find.

The solution to a problem is represented by the following equation:

$$\begin{array}{l}{\left(9.0 \times 10^{9} \mathrm{N} \mathrm{m}^{2} / \mathrm{C}^{2}\right)(0.020 \mathrm{C})(0.050 \mathrm{C}) /(100 \mathrm{m})^{2}} \\ {+\left(9.0 \times 10^{9} \mathrm{N} \mathrm{m}^{2} / \mathrm{C}^{2}\right)(0.010 \mathrm{C})(0.050 \mathrm{C}) /(50 \mathrm{m})^{2}=(10 \mathrm{kg}) a_{x}}\end{array}$$

Sketch a situation that the equation might represent and formulate a problem for which it is a solution (there are multiple possibilities).

A stationary block has a charge of $+6.0 \times 10^{-4} \mathrm{C}$. A 0.80-kg cart with a charge of $+4.0 \times 10^{-4} \mathrm{C}$ is initially at rest and separated by 4.0 m from the block. The cart is released and moves along a frictionless surface to a distance of 10.0 m from the block. Determine as many values of the physical quantities describing the motion of the cart as you can.

How is electric potential energy similar to spring potential energy? How is it different?

An electron is 0.10 cm from an object with electric charge of $+3.0 \times 10^{-3} \mathrm{C}$. (a) Determine the magnitude of the electrical force $F_{\mathrm{O} \text { on } e}$ that the object exerts on the electron. (b) The electron is pulled so that it moves to a distance of 0.11 cm from the charged object. Determine the magnitude of the electrical force $F_{\mathrm{O} \text { on } e}^{\prime}$ exerted by the charged object on the electron when at this distance. (c) Estimate the work done by the average force pulling the electron $\left(\frac{F_{\mathrm{O} \text { on } e}+F_{\mathrm{O} \text { on } e}^{\prime}}{2}\right) \Delta x$ (d) Compare this number to the change in electric potential energy of the electron–charged-object system as the electron moves away from the object. Why should the numbers be approximately equal?

Two balloons of different mass hang from strings near each other. You charge them about the same amount by rubbing each balloon with wool. Draw a force diagram for each of the balloons. Compare the angles of the threads with the vertical. How do your answers depend on whether the balloons have the same or different magnitude charge?

Which explanation agrees with the contemporary model of electric charge?(a) If an object is charged negatively by rubbing, it has lost positively charged particles.(b) If an object is charged positively by rubbing, it has lost negatively charged particles.(c) If an object is charged positively by rubbing, it has acquired positively charged particles.(d) If an object is charged negatively by rubbing, it has acquired negatively charged particles.(e) a and c (f) b and d

The metal sphere on the top of a Van de Graaff generator has a relatively large positive charge. In which direction must a positively charged ion in the air move relative to the sphere in order for the electrical energy the ion-generator system to decrease? Justify your answer.

Why isn’t Coulomb’s law valid for large conducting or dielectric objects, even if they are spherically symmetrical?

The electrical force that one electric charge exerts on another is proportional to the product of their charges—that is, $F_{1 \mathrm{on} 2} \propto q_{1} q_{2}$. How would Coulomb’s observations be different if the force were proportional to the sum of their charges

At one instant of time, a person’s heart has a dipolar charge on it, with a positive charge on the bottom and a negative charge on the top of the heart. Will the electric potential energy of a sodium ion (charge $+e$) on the left side of the heart (as seen by another person) and at a level halfway between the heart’s charges increase, decrease,or remain the same if the sodium ion moves up? What will happen to the potential energy of a chlorine ion (charge $-e$) that starts at the same place and moves up? Justify each answer.

Describe the experiments that were first used to determine a quantitative expression for the magnitude of the force that one electrically charged object exerts on another electrically charged object. What are the limitations of this expression?

Two metal balls of the same radius are placed a small distance apart. Will they interact with the same magnitude force when they have like charges as when they have opposite charges? Explain your answer. Include a sketch showing the charge distribution.

You have a system of two negatively charged objects separated by some arbitrary finite distance. (a) What is the sign of their potential energy? (Remember that charges that are infinitely far from each other have zero potential energy.) (b) What can you do to decrease this energy? (c) Draw an energy bar chart for this process of decreasing the energy.