Exam 21: Electric Potential

A small 4.0-µC charge and a small 1.5-µC charge are initially very far apart. How much work does it take to bring them to a final configuration in which the 4.0-µC charge is at the point x = 1.0 mm, y = 1.0 mm, and the 1.5-µC charge is at the point x = 1.0 mm, y = 3.0 mm? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

Each plate of an ideal air-filled parallel-plate capacitor has an area of 0.0010 $m ^ { 2 }$ , and the separation of the plates is $0.050 \mathrm {~mm}$ An electric field of $7.4 \times 10^6 \mathrm {~V} / \mathrm { m }$ is present between the plates. What is the capacitance of this capacitor? (ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

When the potential difference between the plates of an ideal air-filled parallel plate capacitor is 35 V, the electric field between the plates has a strength of 750 V/m. If the plate area is 4.0 × 10^-2 m², what is the capacitance of this capacitor? (ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

A proton is accelerated from rest through a potential difference V₀ and gains a speed v₀. If it were accelerated instead through a potential difference of 2V₀, what speed would it gain?

Measurements show that it takes 0.30 mJ of work to move 5.0-μC of charge from one plate to another of a certain air-filled capacitor while the potential difference between these plates is kept constant. What is the potential difference between the plates of this capacitor?

Doubling the capacitance of a capacitor that is holding a constant charge causes the energy stored in that capacitor to

After a proton with an initial speed of 1.50 × 10⁵ m/s has increased its speed by accelerating through a potential difference of 0.100 kV, what is its final speed? (e = 1.60 × 10^-19 C , m_proton = 1.67 × 10^-27 kg)

A +3.0-µC point charge is initially extremely far from a positive point charge Q. You find that it takes 41 J of work to bring the +3.0-µC charge to the point x = 3.0 mm, y = 0.0 mm and the point charge Q to the point x = -3.0 mm, y = 0.00 mm. What is Q? (k = …)

If the electric field between the plates of a given air-filled capacitor is weakened by removing charge from the plates, the capacitance of that capacitor

The plates of a parallel-plate capacitor are maintained with constant potential by a battery as they are pulled apart. During this process, the amount of charge on the plates

A point charge of +3.00 μC and a second charge Q are initially very far apart. If it takes $29.0 \mathrm {~J}$ of work to bring them to a final configuration in which the $+ 3.00 - \mu C$ charge is at the point x = 1.00 mm, y = 1.00 mm, and the second charge Q is at the point x = 1.00 mm, y = 3.00 mm, find the magnitude of the charge Q. (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

The figure shows a group of three particles, all of which have charge Q = 8.8 nC. How much work did it take to assemble this group of charges if they all started out extremely far from each other? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

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 and charged until its plates carry charges +Q and -Q, and the battery is then disconnected. If the separation between the plates is now doubled, the electrical energy stored in the capacitor will

At a distance d from a point charge Q, the energy density in its electric field is u. If we now go to a distance d/2 from the charge, what is the energy density at the new location?

At a distance d from a point charge Q, the energy density in its electric field is u. If we double the charge, what is the energy density at the same point?

Three point charges are placed at the following points in a horizontal x-y plane: $+ 4.0 \mu \mathrm { C }$ is at $( 0.00 \mathrm {~m} , 0.50 \mathrm {~m} )$ $+ 1.0 \mu \mathrm { C }$ is at $( 0.20 \mathrm {~m} , 0.00 \mathrm {~m} )$ and $- 5.0 \times \mu C$ is at $( 0.20 \mathrm {~m} , 0.50 \mathrm {~m} )$ Calculate the electrical potential (relative to infinity) at the origin due to these three point charges. (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

What the electric energy density at a point 1.0 cm from a proton? (e = 1.6 × 10-19 C, ε₀ = 8.85 × 10^-12 C²/N ∙ m², k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

A 12.0-V battery (potential source) is connected across a 6.00-µF air-filled capacitor. (a) How much energy can be stored this way? (b) How much excess charge is on each plate of the capacitor?

The potential difference between two square parallel plates is 4.00 V. If the plate separation is 6.00 cm and they each measure 1.5 m by 1.5 m, what is the magnitude of the electric field between the plates?

The figure shows an arrangement of two particles each having charge Q = -6.8 nC and each separated by 5.0 mm from a proton.If the two particles are held fixed at their locations and the proton is set into motion as shown, what is the minimum speed the proton needs to totally escape from these particles? (m_proton = 1.67 × 10^-27 kg, e = 1.60 × 10^-19 C, k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)