25. Electric Potential

An electron starting from rest acquires 4.8 keV of kinetic energy in moving from point A to point B. Determine the ratio of their speeds at the end of their respective trajectories.

INT The surface charge density on an infinite charged plane is −2.0×10⁻⁶ C/m². A proton is shot straight away from the plane at 2.0×10⁶ m/s. How far does the proton travel before reaching its turning point?

Two positive point charges are 5.0 cm apart. If the electric potential energy is 72 μJ, what is the magnitude of the force between the two charges?

Two point charges are fixed 4.0 cm apart from each other. Their charges are Q₁ = Q₂ = 6.5 μC and their masses are m₁ = 2.5 mg and m₂ = 3.5 mg. If Q₁ is released from rest, what will be its speed after a very long time?

Two point charges are fixed 4.0 cm apart from each other. Their charges are Q₁ = Q₂ = 6.5 μC and their masses are m₁ = 2.5 mg and m₂ = 3.5 mg. If both charges are released from rest at the same time, what will be the speed of Q₁ after a very long time? Ignore the environment.

Two identical +5.5 μC point charges are initially spaced 8.5 cm from each other. If they are released at the same instant from rest, how fast will they be moving when they are very far away from each other? Assume they have identical masses of 1.0 mg.

(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.

Near the surface of the Earth there is an electric field of about 150 V/m which points downward. Two identical balls with mass m = 0.550 kg are dropped from a height of 2.00 m, but one of the balls is positively charged with q₁ = 650 μC, and the second is negatively charged with q₂ = -650 μC. Use conservation of energy to determine the difference in the speeds of the two balls when they hit the ground. (Neglect air resistance.)

(II) An electron starts from rest 34.5 cm from a fixed point charge with Q = -0.125 nC. How fast will the electron be moving when it is very far away?

(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)?

(II) An electron starting from rest acquires 4.8 keV of kinetic energy in moving from point A to point B. How much kinetic energy would a proton acquire, starting from rest at B and moving to point A?

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.]

A manufacturer claims that a carpet will not generate more than 6.0 kV of static electricity. What magnitude of charge would have to be transferred between a carpet and a shoe for there to be a 6.0-kV potential difference between the shoe and the carpet? Approximate the area of the shoe and assume the shoe and carpet are large sheets of charge separated by a small distance d = 1.0 mm.

A proton with an initial speed of 800,000 m/s is brought to rest by an electric field. What was the potential difference that stopped the proton?

The volume charge density ρ_E within a sphere of radius r₀ is distributed according to the following spherically symmetric relation ρ_E(r) = ρ₀ [ 1 - (r²/ r²₀)] where r is measured from the center of the sphere and ρ₀ is a constant. For a point P inside the sphere ( r < r₀), determine the electric potential V. Let V = 0 at infinity. [Hint: Start with Gauss’s law.]