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Chapter 29: The Electric Potential

Electric Potential Energy

•Kinetic Energy (K): the sum of the kinetic energies of all the particles in the

system.

•K = ½ mv2

•Potential Energy (U): the interaction energy of the system.

•∆U = -Winteraction forces

•W = F∆rcosθ, where ∆r is a linear displacement and θ is between the force and

∆r.

•Conservative Force: the work done as a particle moves from position i (start) to

position f (end) and is independent of the path followed.

•∆Ugrav = -Wgrav = mgyf – mgyi

•∆Uelec = -Welec = qEsf – qEsi

•Electric Potential Energy in a Uniform Electric Field: Uelec = U0 + qEs, where s is

measured from the negative plate and U0 is the potential energy at the

negative plate (s = 0).

•In a parallel-plate capacitor, the potential energy of a positive charge decreases

in the direction of E but the charge gains kinetic energy as it moves toward the

negative plate.

•In a parallel-plate capacitor, the potential energy of a negative charge

decreases in the direction opposite to E and the charge gains kinetic energy as

it moves away from the negative plate.

•If a charged particle is projected outward in a uniform field, it gradually slows

(kinetic to potential) until reaching the turning point where Uelec = Emech.

•If the motion of a particle is always perpendicular to the electric force, the work

done on the charged particle is zero.

The Potential Energy of Point Charges

•Potential Energy of the Two-Point-Charge System: Uelec = Kq1q2/x = 1/(4πε0) x

(q1q2/r), where r is the distance between their centers.

•Two like charges shot toward each other will gradually slow down because of

the repulsive force between them, until the distance between them is rmin, the

distance of closest approach.

•Two oppositely charged particles shot apart from each other with equal but

opposite momenta will slow down, losing kinetic energy until reaching

maximum separation rmax.

•The work is independent of the path; thus, the electric force is a conservative

force.

•Escape Velocity: the initial velocity that allows a particle to reach rf = ∞ with vf

= 0.

•The potential energy of two charged particles approaches zero as r ∞.

•Conservation of Energy: Kf + Uf = Ki + Ui

•If more than two charges are present, the potential energy is the sum of the

potential energies due to all pairs of charges: Uelec = Σ(Kqiqj/rij), where rij is the

distance between qi and qj.

The Potential Energy of a Dipole

•Udipole = -pEcosφ = -pE

•Stable Equilibrium: potential energy is minimum at φ = 0° where the dipole is