Chapter 25 – The Electric Potential

These question-and-answer flashcards review key definitions, formulas, and concepts from Chapter 25 (Electric Potential), including potential energy, work, electric potential, uniform fields, capacitors, point charges, superposition, and energy conservation.

How is the kinetic energy of a system of particles defined?

It is the sum of the individual kinetic energies, K = Σ(½ mᵢ vᵢ²).

What is potential energy in the context of a physical system?

The interaction energy stored in the system due to conservative forces.

What is the relationship between the change in potential energy (ΔU) and the work done by conservative interaction forces?

ΔU = −W_interaction (from initial to final states).

Under what condition is the total mechanical energy K + U conserved?

When only conservative forces (e.g., gravity, electric) act on the system.

What is the formula for the work done by a constant force F acting through a displacement Δr at angle θ?

W = F Δr cos θ = F·Δr.

What expression gives gravitational potential energy near Earth’s surface?

U_grav = m g y (relative to a chosen zero-level).

In a uniform electric field, what constant force acts on a charge q?

F = q E.

How much work is done when a charge q moves a distance s parallel to a uniform electric field E?

W_elec = q E s.

What is the electric potential energy of a charge q at a position s inside a uniform field (measured from the negative plate)?

U_elec = q E s.

For a positive charge moving toward the negative plate in a capacitor, how do kinetic and potential energies change?

Kinetic energy increases while electric potential energy decreases.

For a negative charge moving with the electric field toward the positive plate, what happens to its energies?

It slows down; kinetic energy decreases as electric potential energy increases (becomes less negative).

What does an energy diagram for a positive charge in a uniform electric field illustrate?

Potential energy increases linearly with distance, but total mechanical energy remains constant.

What is the electric potential energy of two point charges q₁ and q₂ separated by a distance r?

U = k q₁ q₂ / r = (1/4π ε₀) q₁ q₂ / r.

As the separation between two point charges approaches infinity, what happens to their potential energy?

It approaches zero.

For two like charges with positive total mechanical energy, what determines their distance of closest approach r_min?

They slow until K = 0 at rmin where U = Emech.

For two opposite charges fired apart with Emech < 0, what is their maximum separation rmax?

It is reached when kinetic energy becomes zero and U equals E_mech.

Why is the electric force classified as a conservative force?

Because the work it does depends only on initial and final positions, not on the path taken.

How do you calculate the total potential energy of a system with more than two point charges?

U = Σ{i

How is electric potential V defined in terms of potential energy?

V = U_(q+sources) / q (potential energy per unit charge due to source charges).

What is the SI unit of electric potential and its definition?

The volt (V); 1 V = 1 joule per coulomb (1 J/C).

Does the value of electric potential depend on the magnitude of a test charge used to measure it?

No; V is a property of the source charges and is independent of the test charge.

State the energy-conservation equation for a charged particle moving through a potential difference.

Kf + q Vf = Ki + q Vi.

Inside a parallel-plate capacitor, how is electric potential related to distance s from the negative plate?

V = E s.

What is the potential difference (voltage) between the plates of a capacitor of plate separation d?

ΔV = E d.

What alternative unit can express electric-field strength besides N/C?

Volt per meter (V/m); 1 N/C = 1 V/m.

What is the electric potential of a point charge q at distance r (with V = 0 at infinity)?

V = k q / r = (1/4π ε₀) q / r.

Outside a uniformly charged sphere of radius R, what is the electric potential at distance r ≥ R?

V = k Q / r, identical to that of a point charge at the center.

If the potential at the surface of a charged sphere is V₀, what is the potential at distance r ≥ R?

V = V₀ R / r.

What principle allows the calculation of total electric potential from many point charges?

The principle of superposition: V = Σ k qi / ri.

Inside a parallel-plate capacitor, how are electric-field vectors oriented relative to equipotential surfaces?

They are perpendicular to equipotential surfaces and point toward decreasing potential.

Why is the choice of zero electric potential considered arbitrary?

Because only potential differences matter; shifting all potentials by a constant leaves physics unchanged.

What expression relates electric field strength to voltage difference in a capacitor?

E = ΔV / d.

What is the electric potential on the axis of a thin uniformly charged ring (qualitative expression)?

V(z) = k Q / √(R² + z²), showing dependence on distance z from the center.