1. Charge $q_1$ is distance r from a positive point charge Q. Charge $q_2=q_1\text{/}3$ is distance 2r from Q. What is the ratio $U_1\text{/}{U}_2$ of their potential energies due to their interactions with Q?

2. Charge $q_1$ is distance s from the negative plate of a parallel-plate capacitor. Charge $q_2=q_1\text{/}3$ is distance 2s from the negative plate. What is the ratio $U_1\text{/}{U}_2$ of their potential energies?

FIGURE Q25.2 shows the potential energy of a proton $(q=+e)$ and a lead nucleus $(q=+82e)$. The horizontal scale is in units of femtometers, where $1\text{fm}={10}^{-15}\text{m}$.

FIGURE Q25.2

1. A proton is fired toward a lead nucleus from very far away. How much initial kinetic energy does the proton need to reach a turning point 10 fm from the nucleus? Explain.

2. How much kinetic energy does the proton of part a have when it is 20 fm from the nucleus and moving toward it, before the collision?

An electron moves along the trajectory of FIGURE Q25.3 from i to f.

FIGURE Q25.3

1. Does the electric potential energy increase, decrease, or stay the same? Explain.

2. Is the electron’s speed at f greater than, less than, or equal to its speed at i? Explain.

Two protons are launched with the same speed from point 1 inside the parallel-plate capacitor of FIGURE Q25.4. Points 2 and 3 are the same distance from the negative plate.

FIGURE Q25.4

1. Is $\text{Δ}{U}_{1\to 2}$, the change in potential energy along the path $1\to 2$, larger than, smaller than, or equal to $\text{Δ}{U}_{1\to 3}?$

2. Is the proton’s speed $v_2$ at point 2 larger than, smaller than, or equal to $v_3?$ Explain.

Rank in order, from most positive to most negative, the potential energies $U_{\text{A}}$ to $U_{\text{F}}$ of the six electric dipoles in the uniform electric field of FIGURE Q25.5. Explain.

FIGURE Q25.5

FIGURE Q25.6 shows the electric potential along the x-axis.

FIGURE Q25.6

1. Draw a graph of the potential energy of a 0.1 C charged particle. Provide a numerical scale for both axes.

2. If the charged particle is shot toward the right from $x=1\text{m}$ with 1.0 J of kinetic energy, where is its turning point? Use your graph to explain.

A capacitor with plates separated by distance d is charged to a potential difference $\text{Δ}{V}_{\text{C}}$. All wires and batteries are disconnected, then the two plates are pulled apart (with insulated handles) to a new separation of distance 2d.

1. Does the capacitor charge Q change as the separation increases? If so, by what factor? If not, why not?

2. Does the electric field strength E change as the separation increases? If so, by what factor? If not, why not?

3. Does the potential difference $\text{Δ}{V}_{\text{C}}$ change as the separation increases? If so, by what factor? If not, why not?

Rank in order, from largest to smallest, the electric potentials $V_1$ to $V_5$ at points 1 to 5 in FIGURE Q25.8. Explain.

FIGURE Q25.8

FIGURE Q25.9 shows two points inside a capacitor. Let $V=0\text{V}$ at the negative plate.

FIGURE Q25.9

1. What is the ratio $V_2\text{/}{V}_1$ of the electric potentials? Explain.

2. What is the ratio $E_2\text{/}{E}_1$ of the electric field strengths?

FIGURE Q25.10 shows two points near a positive point charge.

FIGURE Q25.10

1. What is the ratio $V_2\text{/}{V}_1$ of the electric potentials? Explain.

2. What is the ratio $E_2\text{/}{E}_1$ of the electric field strengths?

FIGURE Q25.11 shows three points near two point charges. The charges have equal magnitudes. For each part, rank in order, from most positive to most negative, the potentials $V_1$ to $V_3$.

FIGURE Q25.11

Full Alternative Text

Reproduce FIGURE Q25.12 on your paper. Then draw a dot (or dots) on the figure to show the position (or positions) at which the electric potential is zero.

FIGURE Q25.12