Work done by a constant force If the force is parallel to the displacement If the force is not paralell to the displacement Vectorial notation

Work done by a varying force In general the work depends on the path between A and B

Potential Energy In a conservative field the work done by the field does not depend on the path Friction and applied forces are not conservatives Gravity is conservative The electrostatic field is conservative

Work done by the field and a external applied force Work done by the field when a charge q moves from A to B= decrease of potential energy (something falls): Work done by an applied force to move q from A to B = increase of potential energy (hand raises something):

Potential In a conservative field the work done by the field does not depend on the path

Electric potential and electric field Potential: Potential energy of q per unit charge Electric field: Force on q per unit charge Unit: Volt=Joule/Coulomb V=J/C Unit: Newton/Coulomb=Volt/meter N/C=V/m

Potential landscapes Positive charge Negative charge

Potential: summary thus far Charges CREATE potential landscapes Charges FEEL potential landscapes We work with  U or  V because only changes matter

Creating potentials: Two examples

Remember: electric field created by a point charge Q has the direction and sense of the force on a positive charge

Potential created by a point charge Take V=0 at r= 

Potential of a constant field Created by planar distributions of charge  l : displacement in the direction and sense of the field