Physics 014 Electric fields 1

Topics Electric Field Electric Field Lines Electric Fields due to points, dipoles, etc.

Electric Field How do we deal with action at a distance?

Electric Field Using a vector field, we can describe action at a distance near a charged object:

Electric Field We define the electric field, at point P due to the charged object as

Electric Field The force on a test charge q0 DUE to an external field is

Electric Field Using a vector field, we can describe action at a distance near a charged object: Place a positive test charge q0 near the object at point P Measure the electrostatic force acting on the charge:

Electric Field The magnitude of the electric field is E=F/q0 The SI unit for electric field is newton per coulomb (N/C)

Electric Field Lines Electric field lines are a useful visual way of picturing electric fields

Electric Field Lines At any point, the direction of a straight field line gives the direction of the electric field at that point

Electric Field Lines At any point, the direction of the tangent to curved lines gives the direction of the electric field at that point.

Electric Field Lines Electric field lines extend away from positive charge (where they originate) and toward negative charges (where they terminate)

Electric Field Lines The electric field is: large where field lines are close together small where they are apart

E due to a point charge The magnitude of the electric field due to a point charge is

E due to a point charge F is from Coulomb’s law The vector points away from the point charge, q, if q is positive The vector points toward the point charge, q, if q is negative

E due to a point charge For a test charge near n point charges, the net electric field at the position of the test charge is

??? For a proton p and an electron e on an x axis, what is the direction of the electric field due to the electron at (a) point S and (b) point R? What is the direction of the net electric field at (c) point R and (d) point S?

E due to a point charge Example: The diagram shows three particles with charges q1=+2Q, q2=2Q, and q3=-4Q, each a distance d from the origin. What net electric field is produced at the origin?

Given: Eqn: q1=+2Q q2=-2Q q3=-4Q = ?

Calc: First we will find the fields due to the individual charges, the we will do a vector sum to find the net electric field.

Calc: Now we do a vector sum for the net electric field

Calc: There is an easy way to do the vector sum. Use symmetry. Notice that E1 +E2 equals the magnitude E3. In addition, from the diagram we see that and are symmetric about the x axis; their y components cancel

Calc: By symmetry,