25. Electric Potential

(II) An electron starting from rest acquires 4.8 keV of kinetic energy in moving from point A to point B.

(b) Determine the ratio of their speeds at the end of their respective trajectories.

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.

(a) 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.

(b) 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.

(II) 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?

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.

One possible form for the potential energy (U) of a diatomic molecule (Fig. 40–8) is called the Morse Potential:

U = U₀ [1 - e⁻ᵃ⁽ʳ ⁻ ʳᵒ⁾]².

(a) Show that r₀ represents the equilibrium distance and U₀ the dissociation energy.

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One possible form for the potential energy (U) of a diatomic molecule (Fig. 40–8) is called the Morse Potential:

U = U₀ [1 - e⁻ᵃ⁽ʳ ⁻ ʳᵒ⁾]².

(b) Graph U from r = 0 to r = 4r₀, assuming a = 18nm⁻¹, U₀ = 4.6 eV, and r₀ = 0.13 nm

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A simple picture of an H₂ molecule sharing two electrons is shown in Fig. 40–56. We assume the electrons are symmetrically located between the two protons, which are separated by r₀ = 0.074 nm. (a) When the electrons are separated by a distance d, write the total potential energy U in terms of d and r_0

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A simple picture of an H₂ molecule sharing two electrons is shown in Fig. 40–56. We assume the electrons are symmetrically located between the two protons, which are separated by r₀ = 0.074 nm. (c) Determine analytically the value of d that gives minimum U (greatest stability).

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