Exam 21: Electric Potential

Two protons are released from rest, with only the electrostatic force acting. Which of the following statements must be true about them as they move apart? (There could be more than one correct choice.)

Four +6.00-µC point charges are at the corners of a square 2.00 m on each side. What is the electric potential of these charges, relative to infinity, at the center of this square? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

A +7.5-nC point charge is 5.0 cm from a -9.4-µC point charge in your laboratory in California. How much work would you have to do if you left the +7.5-nC charge in the lab but took the -9.4-µC charge to New York City? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

Two very large parallel metal plates, separated by 0.20 m, are connected across a 12-V source of potential. An electron is released from rest at a location 0.10 m from the negative plate. When the electron arrives at a distance 0.050 m from the positive plate, how much kinetic energy has the electron gained? (e = 1.60 × 10^-19 C)

A parallel-plate capacitor consists of a set of two parallel plates of area A separated by a distance d. This capacitor is connected to a battery that maintains a constant potential difference across the plates. A slab of a dielectric material is inserted in the region between the plates and completely fills it. What changes would you observe as the dielectric is inserted? (There could be more than one correct choice.)

An air-filled capacitor has a potential difference between the plates of 80 V. If the charge on each of the plates of the capacitor has magnitude 8.0 μC, what is the electrical energy stored by this capacitor?

The potential difference between the plates of an ideal air-filled parallel-plate capacitor with a plate separation of 6.0 cm is 60 V. What is the strength of the electric field between the plates of this capacitor?

Which of the following will increase the capacitance of a parallel-plate capacitor? (There could be more than one correct choice.)

A square is 1.0 m on a side. Point charges of +4.0 μC are placed in two diagonally opposite corners. In the other two corners are placed charges of +3.0 μC and -3.0 μC. What is the potential (relative to infinity) at the midpoint of the square? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

A proton that is initially at rest is accelerated through an electric potential difference of magnitude 500 V. What speed does the proton gain? (e = 1.60 × 10^-19 C , m_proton = 1.67 × 10^-27 kg)

A 15-μF capacitor is connected to a 50-V battery and becomes fully charged. The battery is removed and a slab of dielectric, having a dielectric constant of 5.0, is inserted between the plates and completely fills the space between them. (a) What is the capacitance of the capacitor after the slab is inserted? (b) What is the potential difference across the capacitor with the dielectric inserted.

Two protons are fired toward each other in a particle accelerator, with only the electrostatic force acting. Which of the following statements must be true about them as they move closer together? (There could be more than one correct choice.)

As an electron moves in the direction the electric field lines

Two 5.0-µC point charges are 12 cm apart. What is the electric potential (relative to infinity) of this combination at the point where the electric field due to these charges is zero? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

The electric potential at a distance of 4 m from a certain point charge is 200 V relative to infinity. What is the potential (relative to infinity) at a distance of 2 m from the same charge?

Consider a uniform horizontal electric field of 50 N/C directed toward the east. If the electric potential at a given point in the field is 80 V, what is the potential at a point 1.0 m directly east of the point?

A proton with a speed of 2.0 x $10^5$ m/s accelerates through a potential difference and thereby increases its speed to 4.0 x $10^5$ m/s. Through what magnitude potential difference did the proton accelerate? (e = 1.60 × 10^-19 C , m_proton = 1.67 × 10^-27 kg)

What charge accumulates on the plates of a 2.0-μF air-filled capacitor when it is charged until the potential difference across its plates is 100 V?

As a proton moves in a direction perpendicular to the electric field lines

An ideal parallel-plate capacitor consists of two parallel plates of area A separated by a distance d. This capacitor is connected across a battery that maintains a constant potential difference between the plates. If the separation between the plates is now doubled, the magnitude of the charge on the plates will