25. Electric Potential

A +38 μC point charge is placed 36 cm from an identical +38 μC charge. Then a -1.8 μC charge is moved from point A to point B as shown in Fig. 23–50. What is the change in potential energy?

The electric field strength is 50,000 N/C inside a parallel-plate capacitor with a 2.0 mm spacing. A proton is released from rest at the positive plate. What is the proton's speed when it reaches the negative plate?

For three point charges, $q_1$, $q_2$, and $q_3$, placed at the corners of a triangle with distances $r_{12}$, $r_{13}$, and $r_{23}$ between them, what is the total electric potential energy of the system?

Given three point charges $q_1$, $q_2$, and $q_3$ located at the vertices of a triangle with distances $r_{12}$, $r_{13}$, and $r_{23}$ between them, what is the total electric potential energy of the system?

When two like point charges are moved farther apart from each other, what happens to their electric potential energy ($U$)?

A proton is accelerated from rest through a potential difference and acquires a kinetic energy of $3.2\times {10}^{\mathrm{-16}}$ J. What potential difference is required to bring the proton to rest?

In the context of two point charges, when does the electric potential energy $U$ increase as the distance $r$ between them increases?

Which formula is used to calculate the amount of electric heat produced by an electric furnace, assuming all electrical energy is converted to heat?

Two equal positive point charges are placed at different distances from each other. Which configuration has more electric potential energy: when the charges are closer together or farther apart? $U=\frac{k{q}_1{q}_2}{r}$

(II) Many chemical reactions release energy. Suppose that at the beginning of a reaction, an electron and a proton are separated by 0.110 nm, and their final separation is 0.100 nm. How much electric potential energy was lost in this reaction (in units of eV)?

The liquid-drop model of the nucleus suggests that high-energy oscillations of certain nuclei can split (“fission”) a large nucleus into two unequal fragments plus a few neutrons. Using this model, consider the case of a uranium nucleus fissioning into two spherical fragments, one with a charge q₁ = +38e and radius r₁ = 5.5 x 10⁻¹⁵ m, the other with q₂ = + 54e and r₂ = 6.2 x 10⁻¹⁵ m. Calculate the electric potential energy (MeV) of these fragments, assuming that the charge is uniformly distributed throughout the volume of each spherical nucleus and that their surfaces are initially in contact at rest. The electrons surrounding the nuclei can be neglected. This electric potential energy will then be entirely converted to kinetic energy as the fragments repel each other. How does your predicted kinetic energy of the fragments agree with the observed value associated with uranium fission (approximately 200 MeV total)? [ 1 MeV = 10⁶ eV.]

Given three point charges, $q_1$, $q_2$, and $q_3$, located at the vertices of a triangle with distances $r_{12}$, $r_{13}$, and $r_{23}$ between them, what is the total electric potential energy of the system?

The electric potential is 40 V at point A near a uniformly charged sphere. At point B, 2.0 μm farther away from the sphere, the potential has decreased by 0.16 mV. How far is point A from the center of the sphere?

(III) Determine the total electrostatic potential energy of a conducting sphere of radius r₀ that carries a total charge Q distributed uniformly on its surface.