Exam 21: Electric Potential

In a region where the electric field is uniform and points in the +x direction, the electric potential is -2000 V at x = 8 m and is +400 V at x = 2 m. What is the magnitude of the electric field?

A hydrogen atom consists of a proton and an electron. If the orbital radius of the electron increases, the electric potential energy of the electron due to the proton

Point charges +4.00 μC and +2.00 μC are placed at the opposite corners of a rectangle as shown in the figure. What is the potential at point A, relative to infinity, due to these charges? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

A 12.6-µF isolated capacitor is constructed with Teflon, having a dielectric constant of 2.1, between the plates. The capacitor is initially charged to 1.5 volts, and then the Teflon is removed. (a) How much excess charge was originally stored on the plates of the capacitor? (b) After removing the Teflon, what is the potential difference across the capacitor plates?

An ideal parallel-plate capacitor having circular plates of diameter D that are a distance d apart stores energy U when it is connected across a fixed potential difference. If you want to triple the amount of energy stored in this capacitor by changing only the size of its plates, the diameter should be changed to

If a Cu²⁺ ion that is initially at rest accelerates through a potential difference of 12 V without friction, how much kinetic energy will it gain? (e = 1.60 × 10^-19 C)

A uniform electric field, with a magnitude of 500 V/m, is points in the +x direction. If the potential at x = 5.0 m is 2500 V, what is the potential at x = 2.0 m?

Each plate of an ideal air-filled parallel-plate capacitor has an area of 0.0020 $m ^ { 2 }$ , and the separation of the plates is $0.090 \mathrm {~mm}$ An electric field of $2.1 \times 10^6 \mathrm {~N} / \mathrm { C }$ is present between the plates. What is the surface charge density on the plates? (ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

An ideal, isolated, air-filled parallel-plate capacitor is not connected to a battery but has equal and opposite charges of 3.9 nC on its plates. The separation between the plates initially is 1.2 mm, and for this separation the capacitance is 3.1 × 10^-11 F. How much work must be done to pull the plates apart until their separation becomes 7.7 mm? (ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

A 6.9 μC negative point charge has a positively charged particle in an elliptical orbit about it. If the mass of the positively charged particle is $1.0 \mu \mathrm { g }$ and its distance from the point charge varies from $4.0 \mathrm {~mm}$ to $16.0 \mathrm {~mm}$ , what is the maximum potential difference through which the positive object moves? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

A very small 4.8-g particle carrying a charge of +9.9 μC is fired with an initial speed of $8.0 \mathrm {~m} / \mathrm { s }$ directly toward a second small 7.8-g particle carrying a charge of + $5.2 \mu \mathrm { C } \text {. }$ The second particle is held fixed throughout this process. If these particles are initially very far apart, what is the closest they get to each other? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

An ideal air-filled parallel-plate capacitor with horizontal plates has a plate separation of 5.0 cm. If the potential difference between the plates is 2000 V, with the top plate at the higher potential, what are the magnitude and direction of the electric field between the plates?

An electron is released from rest at a distance of 9.00 cm from a fixed proton. How fast will the electron be moving when it is 3.00 cm from the proton? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C², e = 1.60 × 10^-19 C, m_electron = 9.11 × 10^-31 kg, m_proton = 1.67 × 10^-27 kg)

The square plates of a 3000-pF parallel-plate capacitor measure 40 mm by 40 mm and are separated by a dielectric that is 0.29 mm thick and completely fills the region between the plates. What is the dielectric constant of the dielectric? (ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

Point charges +4.00 μC and +2.00 μC are placed at the opposite corners of a rectangle as shown in the figure. What is the potential at point B due to these charges? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

An alpha particle (a helium nucleus, having charge +2e and mass 6.64 × 10^-27 kg) moves head-on at a fixed gold nucleus (having charge +79e). If the distance of closest approach is 2.0 × 10^-10 m, what was the speed of the alpha particle when it was very far away from the gold? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C², e = 1.60 × 10^-19 C)

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 south of that point?

When a 4-μF capacitor has a potential drop of 20 V across its plates, how much electric potential energy is stored in this capacitor?

An capacitor consists of two large parallel plates of area A separated by a very small distance d. This capacitor is connected to a battery and charged until its plates carry charges +Q and -Q, and then disconnected from the battery. If the separation between the plates is now doubled, the potential difference between the plates will

If the result of your calculation of a quantity has SI units kg ∙ m²/(s² ∙C), that quantity could be