PHYA22 Chapter 27.doc

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12 Mar 2012
Chapter 27: The Electric Field
Electric Field Models
Four Widely Used Electric Field Models:
oThe electric field of a point charge
oThe electric field of an infinitely long charged wire
oThe electric field of an infinitely wide charged plane
oThe electric field of a charged sphere
Electric Field of a Point Charge: E = 1/(4π ε 0) x q/r2 x r^, where r^ is a unit
vector pointing away from q and ε0 = 8.85 x 10-12 C2/Nm2.
E = Fon q/q
The net electric field is the vector sum of the electric fields due to each charge
and obeys the principle of superposition.
Electric field very far away from charged objects appears to be a point charge
in the distance.
The Electric Field of Multiple Point Charges
Enet = (Enet)xi^ + (Enet)yj^ + (Enet)zk^
To solve,
oFor each charge, determine its distance from P and the angle of Ei from
the axes.
oCalculate the field strength of each charge’s electric field.
oWrite each vector Ei in component form.
oSum the vector components to determine Enet.
oIf needed, determine the magnitude and direction of Enet.
The net electric field far from the source charges: Enet (x >> d) = 1/(4π ε 0) x
3q/x2 x i^
Electric Dipole: formed by two equal but opposite charges separated by a
small distance.
oPermanent Electric Dipole: oppositely charged particles maintain a
small permanent separation.
oInduced Electric Dipole: polarizing a neutral atom with an external
electric field.
oDipole Moment (p): p = qs, from the negative to the positive charge,
where s is a small distance and unit of dipole moment is in Cm.
Electric Field on the Axis of an Electric Dipole: Edipole = 1/(4π ε 0) x 2p/r3, where
r is the distance measured from the center of the dipole.
Electric Field on Perpendicular Plane (r >> s): Edipole = -1/(4π ε 0) x p/r3, only
half the strength of the on-axis field at the same distance.
Drawing and Using Electric Field Lines
oElectric field lines are continuous curves drawn tangent to the electric
field vectors.
oThe electric field vector at any point is tangent to the field line at that
oClosely spaced field lines represent a larger field strength, with longer
field vectors; widely spaced lines indicate a smaller field strength.
oElectric field lines never cross.
oElectric field lines start from positive charges and end on negative
The Electric Field of a Continuous Charge Distribution
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