Exam 21: Electric Potential

A battery maintains the electrical potential difference of 6.0-V between two large parallel metal plates separated by 1.0 mm. What is the strength of the electric field between the plates?

The potential (relative to infinity) at the midpoint of a square is 3.0 V when a point charge of +Q is located at one of the corners of the square. What is the potential (relative to infinity) at the center when each of the other corners is also contains a point charge of +Q?

A 5.0 μF capacitor has a potential difference of $5.0 \mathrm {~V}$ applied across its plates. If the potential difference across its plates is increased to $8.0 \mathrm {~V}$ how much additional energy does the capacitor store?

A parallel-plate capacitor consists of two parallel, square plates having dimensions 1.0 cm by 1.0 cm. The plates are separated by $1.0 \mathrm {~mm}$ and the space between them is filled with Teflon, which has a dielectric constant of 2.1. What is the capacitance of this capacitor? (ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

A parallel-plate air-filled capacitor is made from two plates that are 0.070 m on each side and spaced 9.2 mm apart. What must the potential difference between the plates be to produce an energy density of $0.062 \mathrm {~J} / \mathrm { m } ^ { 3 }$ in the region between them? (ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

A dielectric material such as paper is inserted between the plates of a capacitor as the capacitor holds a fixed charge on its plates. What happens to the electric field between the plates as the dielectric is inserted?

An air-filled capacitor carries enough charge to store $6.00 \mathrm {~mJ}$ of potential energy. It is then accidentally filled with water in such a way as not to discharge its plates. How much energy does it continue to store after it is filled? The dielectric constant for water is 78 and for air it is 1.0006.

In the figure, +4.0-μC and -4.0-μC point charges are located as shown. Now an additional +2.00-µC point charge is placed at point A. What is the electric potential energy of this system of three charges, relative to infinity? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

A proton and an electron are released from rest, with only the electrostatic force acting. Which of the following statements must be true about them as they move toward each other? (There could be more than one correct choice.)

Two tiny grains of sand having charges of 4.0 μC and -4.0 μC are situated along the x-axis at x₁ = 2.0 m and x₂ = -2.0 m. What is electric potential energy of these grains relative to infinity? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

If the electric potential at a point in space is zero, then the electric field at that point must be

A parallel-plate capacitor with plate separation of 4.0 cm has a plate area of 6.0 × $10^{ - 2}$ $m ^ { 2 }$ .What is the capacitance of this capacitor if a dielectric material with a dielectric constant of 2.4 is placed between the plates, completely filling the space? (ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

Two point charges of +2.00 μC and +4.00 μC are at the origin and at the point x = 0.000 m, y = -0.300 m, as shown in the figure. What is the electric potential due to these charges, relative to infinity, at the point P at x = 0.400 m on the x-axis? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

If the result of your calculations for a quantity has SI units of C² ∙ s²/(kg ∙ m²), that quantity could be

A 7.0-μC point charge and a $9.0 - \mu \mathrm { C }$ point charge are initially extremely far apart. How much work does it take to bring the $7.0 - \mu \mathrm { C }$ point charge to the point $x = 3.0 \mathrm {~mm}$ $y = 0.0 \mathrm {~mm}$ , and the $9.0 - \mu \mathrm { C }$ point charge to the point $x = - 3.0 \mathrm {~mm}$ $y = 0.0 \mathrm {~mm} ?$ (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

A 6.0-μF air-filled capacitor is connected across a 100-V potential source (a battery). After the battery fully charges the capacitor, it is left connected and the capacitor is immersed in transformer oil, which has a dielectric constant of 4.5. How much additional charge flows from the battery onto the capacitor during this process?

How much work is needed to carry an electron from the positive terminal to the negative terminal of a 9.0-V battery. (e = 1.60 × 10^-19 C , m_electron = 9.11 × 10^-31 kg)

Doubling the potential across a given capacitor causes the energy stored in that capacitor to

A spherical oil droplet with nine excess electrons is held stationary in an electric field between two large horizontal plates that are 2.25 cm apart. The field is produced by maintaining a potential difference of 0.3375 kV across the plates, and the density of the oil is 824 kg/m³. What is the radius of the oil drop? (e = 1.60 × 10^-19 C)

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. The charges are all equidistant from the origin. The amount of work required to move a positively charged particle from point P to point O (both of which are on the z-axis) is