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

point.

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

charges.

The Electric Field of a Continuous Charge Distribution