Exam 21: Electric Potential

A 3.0-pFcapacitor consists of two large closely-spaced parallel plates that have surface charge densities of $\pm 1.0 \mathrm { nC } / \mathrm { mm } ^ { 2 }$ If the potential across the plates is $23.0 \mathrm { kV }$ with only air between them, find the surface area of each of the plates. (ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

A proton moves 0.10 m along the direction of an electric field of magnitude 3.0 V/m. What is the change in kinetic energy of the proton? (e = 1.60 × 10^-19 C)

Two isolated copper plates, each of area 0.40 m², carry opposite charges of magnitude 7.08 × 10^-10 C. They are placed opposite each other in parallel alignment, with a spacing of 4.0 cm between them. What is the potential difference between the plates? (ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

If you want to store 2.0 mJ of energy in a 10-μF capacitor, how much potential do you need to put across it?

A capacitor has a voltage of 391 ${~V}$ applied across its plates, and then the voltage source is removed. What is the potential difference across its plates if the space between them is then filled with mica, having a dielectric constant of 5.4?

An air-filled 20-μF capacitor has a charge of 60 μC on its plates. How much energy is stored in this capacitor?

The plates of a parallel-plate capacitor are maintained with constant voltage by a battery as they are pulled apart. What happens to the strength of the electric field between the plates during this process?

An ideal parallel-plate capacitor consists 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. If the separation between the plates is now doubled, the amount of electrical energy stored on the capacitor will

Two +6.0-µC charges are placed at two of the vertices of an equilateral triangle having sides 2.0 m long. What is the electric potential at the third vertex, relative to infinity, due to these charges? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

A -6.5-µC point charge is 8.0 cm from a -17-µC charge. What is the electric energy density at the point midway between them? (ε₀ = 8.85 × 10^-12 C²/N ∙ m², k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

Two tiny particles having charges q₁ = +56.0 nC and ^q₂ = -46.0 nC are separated by $0.500 \mathrm {~m}$ and held in place, as shown in the figure. A third particle, having a charge of $54.0 \mathrm { nC }$ is placed at the point A, which is 0.18 m to the left of ^q₂. How much work is needed to move the third particle from point A to point B, which is 0.40 m to the left of ^q₁. All the points in the figure lie on the same line. (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

A space probe approaches a planet, taking measurements as it goes. If it detects a potential difference of 6000 MV between the altitudes of 253,000 km and 276,000 km above the planet's surface, what is the approximate electric field strength produced by the planet at 264,500 km above the surface? Assume the electric field strength is approximately constant at these altitudes.

A region of space contains a uniform electric field, directed toward the right, as shown in the figure. Which statement about this situation is correct?

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 difference V_A - V_B? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

A +5.0-nC charge is at the point (0.00 m, 0.00 m) and a -2.0-nC charge is at (3.0 m, 0.00 m). What work is required to bring a 1.0-nC charge from very far away to point (0.00 m, 4.0 m)? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

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

The electron-volt is a unit of

Four charged particles (two having a charge +Q and two having a charge -Q) are arranged in the xy-plane, as shown in the figure. These particles are all equidistant from the origin. The electric potential (relative to infinity) at point P on the z-axis due to these particles, is

How much energy is necessary to place three +2.0-µC point charges at the vertices of an equilateral triangle of side 2.0 cm if they started out extremely far away? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

A battery charges a parallel-plate capacitor fully and then is removed. The plates are then slowly pulled apart. What happens to the potential difference between the plates as they are being separated?