Dipole moment and electric field
p = qd
p = dipole moment
q = charge
d = displacement, “í” to “+” charge
23.13 - Gotchas
I increased the amount of the charge of a test charge, and the force exerted on it changed. This means the field I was assessing must have
changed. No. Fields are independent of the test charge. The force increased, in proportion to the test charge, but the original field strength did
not change. The increased force was a result of the increased magnitude of the test charge.
Electric field lines are the same as electric field vectors. No. The direction of the field is tangent to the field lines at any point. In a field diagram
for a point charge, the lines are straight so they do point in the direction of the field. But in many fields the field lines are curved, and the field
vector at any location on a field line is tangent to but distinct from it. Also, field lines and vectors use different conventions for representing field
strength. With vectors, the length is proportional to the strength of the field. In a field diagram, the field lines are closer together in a region with
greater field strength. Although a field diagram is used to represent an electric field, field lines and field vectors are not the same thing.
23.14 - Summary
An electric field is a vector quantity defined throughout a region of three-dimensional
space. It describes the forces that will be experienced by an electric charge if it is
placed at various locations in the field. If a positive charge is introduced, the force
on it equals the field strength times its own charge magnitude, in the direction of the
field. When a negative charge is introduced, the force on it is opposite to the
direction of the field. The field strength is measured in newtons per coulomb (N/C).
A test charge is a small positive charge used to measure a field.
Point charges generate electric fields. At any distance from the charge, the strength
of the field is proportional to the magnitude of the charge and inversely proportional
to the square of the distance from the charge.
An electric field diagram is a convenient means of representing the direction and
strength of an electric field in a region. The direction of a field line represents the
local direction of the electric field. The strength of the field at a particular location is
indicated by the proximity of the field lines to each other around that location.
In an isolated, charged conductor the excess charges distribute themselves on the conductor’s surface in a state of electrostatic equilibrium.
There is no net motion of these charges. The electric field extends perpendicularly outward from all points on the conductor’s surface, and
there is no field inside the conductor.
An electric dipole consists of a positive and a negative charge of equal magnitude, separated by a fixed distance. A vector called the dipole
moment p points from the negative to the positive charge. Its magnitude is equal to the magnitude of either dipole charge times the distance
between the charges. When the dipole is placed in an external electric field, the dipole moment experiences a torque tending to align it in a
direction parallel to the field.
Electric fieldE = F/qtest
Field of a point chargeForce due to an electric field