Conceptual Questions

FIGURE Q26.1 shows the x-component of $\vec{E}$ as a function of x. Draw a graph of V versus x in this same region of space. Let $V =$ 0 V at $x = 0 m$ and include an appropriate vertical scale.

FIGURE Q26.1

FIGURE Q26.1 Full Alternative Text
FIGURE Q26.2 shows the electric potential as a function of x. Draw a graph of $E_{x}$ versus x in this same region of space.

FIGURE Q26.2

FIGURE Q26.2 Full Alternative Text
1. Suppose that $\vec{E} = \vec{0} V / m$ throughout some region of space. Can you conclude that $V = 0 V$ in this region? Explain.
2. Suppose that $V = 0 V$ throughout some region of space. Can you conclude that $\vec{E} = \vec{0} V / m$ in this region? Explain.
Estimate the electric fields $\vec{E}_{1}$ and $\vec{E}_{2}$ at points 1 and 2 in FIGURE Q26.4. Don’t forget that $\vec{E}$ is a vector.

FIGURE Q26.4

FIGURE Q26.4 Full Alternative Text
FIGURE Q26.5 shows two parallel-plate capacitors with the same spacing. Is the electric field strength $E_{1}$ at point 1 larger than, smaller than, or equal to the electric field strength $E_{2}$ at point 2? Explain.

FIGURE Q26.5

FIGURE Q26.5 Full Alternative Text
An electron is released from rest at $x = 2 m$ in the potential shown in FIGURE Q26.6. Does it move? If so, to the left or to the right? Explain.

FIGURE Q26.6

FIGURE Q26.6 Full Alternative Text
FIGURE Q26.7 shows an electric field diagram. Dashed lines A and B are two surfaces in space, not physical objects.
1. Is the electric potential at point 1 higher than, lower than, or equal to the electric potential at point 2? Explain.
2. Rank in order, from largest to smallest, the magnitudes of the potential differences $Δ V_{12}, Δ V_{34}$ , and $Δ V_{56}$ .
3. Is surface A an equipotential surface? What about surface B? Explain why or why not.
FIGURE Q26.7

FIGURE Q26.7 Full Alternative Text
FIGURE Q26.8 shows a negatively charged electroscope. The gold leaf stands away from the rigid metal post. Is the electric potential of the leaf higher than, lower than, or equal to the potential of the post? Explain.

FIGURE Q26.8

FIGURE Q26.8 Full Alternative Text
The two metal spheres in FIGURE Q26.9 are connected by a metal wire with a switch in the middle. Initially the switch is open. Sphere 1, with the larger radius, is given a positive charge. Sphere 2, with the smaller radius, is neutral. Then the switch is closed. Afterward, sphere 1 has charge $Q_{1}$ , is at potential $V_{1}$ , and the electric field strength at its surface is $E_{1}$ . The values for sphere 2 are $Q_{2}, V_{2}$ , and $E_{2}$ .
1. Is $V_{1}$ larger than, smaller than, or equal to $V_{2} ?$ Explain.
2. Is $Q_{1}$ larger than, smaller than, or equal to $Q_{2} ?$ Explain.
3. Is $E_{1}$ larger than, smaller than, or equal to $E_{2} ?$ Explain.
FIGURE Q26.9

FIGURE Q26.9 Full Alternative Text
FIGURE Q26.10 shows a 3 V battery with metal wires attached to each end. What are the potential differences $Δ V_{12} = V_{2} - V_{1}$ , $Δ V_{23} = V_{3} - V_{2}, Δ V_{34} = V_{4} - V_{3}$ , and $Δ V_{41} = V_{1} - V_{4} ?$

FIGURE Q26.10

FIGURE Q26.10 Full Alternative Text
The parallel-plate capacitor in FIGURE Q26.11 is connected to a battery having potential difference $Δ V_{bat}$ . Without breaking any of the connections, insulating handles are used to increase the plate separation to $2 d$ .
1. Does the potential difference $Δ V_{C}$ change as the separation increases? If so, by what factor? If not, why not?
2. Does the capacitance change? If so, by what factor? If not, why not?
3. Does the capacitor charge Q change? If so, by what factor? If not, why not?
FIGURE Q26.11

FIGURE Q26.11 Full Alternative Text
Rank in order, from largest to smallest, the potential differences $(Δ V_{C})_{1}$ to $(Δ V_{C})_{4}$ of the four capacitors in FIGURE Q26.12. Explain.

FIGURE Q26.12

FIGURE Q26.12 Full Alternative Text