25. Electric Potential

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?

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.

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.

Three electrons form an equilateral triangle 1.0 nm on each side. A proton is at the center of the triangle. What is the potential energy of this group of charges?

Three charged particles are placed at the corners of an equilateral triangle that has edge length 2.0 cm. One particle has charge +3.0 nC and a second has charge +6.0 nC. What is the third charge if the electric potential energy of the three charged particles is zero?

How much work would it take to push two protons very slowly from a separation of $2.00\times {10}^{-10}$ m (a typical atomic distance) to $3.00\times {10}^{-15}$ m (a typical nuclear distance)? If the protons are both released from rest at the closer distance in part (a), how fast are they moving when they reach their original separation?

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?

For an electric dipole placed in a uniform external electric field, what orientation of the dipole corresponds to the greatest electric potential energy ($U=\; -pEcos(\theta )$)?

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).

If a charge of $1c$ is moved by the electric force from point $a$ to point $b$, what is the work done by the electric force?

(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?

If two parallel conducting surfaces are separated by a distance $d$ and a potential difference $V$ is applied between them, what is the expression for the distance $d$ in terms of the electric field $E$ and the potential difference $V$?

An electron moves from point i, where the electric potential is $V{i}_{}$, to point f, where the electric potential is $V{f}_{}$. How does the electric potential energy of the electron change as it moves from i to f?