25. Electric Potential

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.]

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?

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

$U=U_0{[1-e^{-a(r-r_0)}]}^2$

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

One possible form for the potential energy (U) of a diatomic molecule (Fig. 40–8) is called the Morse Potential: $U=U_0[1-e^{-a(r-r_0{)}^2}]$. Graph U from r = 0 t o r = 4r₀, assuming a = 18nm^-1, U₀ = 4.6 eV, and r₀ = 0.13 nm.

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. When the electrons are separated by a distance d, write the total potential energy U in terms of d and r₀.

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. Make a graph of U in eV as a function of d in nm.

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. Determine analytically the value of d that gives minimum U (greatest stability).