Learning Objectives

Learning Objectives

Learning Objectives
(See related pages)

Concepts & Skills to Review

gravitational forces (Section 2.6)
gravitational potential energy (Sections 6.4 and 6.5)
Coulomb's law (Section 16.3)
electric field inside a conductor (Section 16.6)
polarization (Section 16.1)

Master the Concepts

Electric potential energy can be stored in an electric field. The electric potential energy of two point charges separated by a distance r is
The signs of q1 and q2 determine whether the electric potential energy is positive or negative. For more than two charges, the electric potential energy is the scalar sum of the individual potential energies for each pair of charges.
The electric potential V at a point is the electric potential energy per unit charge:

In Eq. (17-3), U_E is the electric potential energy due to the interaction of a moveable charge q with a collection of fixed charges and V is the electric potential due to that collection of fixed charges. Both U_Eand V are functions of the position of the moveable charge q.
Electric potential, like electric potential energy, is a scalar quantity. The SI unit for potential is the volt
If a point charge q moves through a potential difference ΔV, then the change in electric potential energy is
The electric potential at a distance r from a point charge Q is
The potential at a point P due to N point charges is the sum of the potentials due to each charge.
An equipotential surface has the same potential at every point on the surface. An equipotential surface is perpendicular to the electric field at all points. No change in electric potential energy occurs when a charge moves from one position to another on an equipotential surface. If equipotential surfaces are drawn such that the potential difference between adjacent surfaces is constant, then the surfaces are closer together where the field is stronger.
The electric field always points in the direction of maximum potential decrease.
The potential difference that occurs when you move a distance d in the direction of a uniform electric field of magnitude E is
The electric field has units of
In electrostatic equilibrium, every point in a conductor must be at the same potential.
A capacitor consists of two conductors (the plates) that are given opposite charges. A capacitor stores charge and electric potential energy. Capacitance is the ratio of the magnitude of charge on each plate (Q) to the electric potential difference between the plates (ΔV). Capacitance is measured in farads (F).
The capacitance of a parallel plate capacitor is

where A is the area of each plate, d is their separation, and _{<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0073512141/663825/efisilin.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (0.0K)</a>} is the permittivity of free space _{<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0073512141/663825/epi.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a><a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0073512141/663825/8854.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (2.0K)</a>} If vacuum separates the plates, k = 1; otherwise, k > 1 is the dielectric constant of the dielectric (the insulating material). If a dielectric is immersed in an external electric field, the dielectric constant is the ratio of the external electric field E0 to the electric field E in the dielectric.
The dielectric constant is a measure of the ease with which the insulating material can be polarized.
The dielectric strength is the electric field strength at which dielectric breakdown occurs and the material becomes a conductor.
The energy stored in a capacitor is
The energy density u—the electric potential energy per unit volume—associated with an electric field is

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