Electric Potential Physics 102 Professor Lee Carkner Lecture 12

PAL #11 Electric Field   Ratio of lines touching 3q to lines touching -1q must be 3 to 1  Extra lines from +3q go to infinity   Positive test charge repelled

PAL #11 Electric Field  To find electric field at a point between the charges:   “q” for the charges is e = 1.6X C,  3q = (3)(1.6X ) =  1q = (1)(1.6X ) =  Measure r (convert to m)   Since both fields point the same way (to the right), add them up

Electrical Force and Energy  Like any other force, the electrical force can do work:  If a force does work, the potential energy must decrease   Let us represent PE as U  Decrease in PE (  U) equal to the work   Energy is conserved

Potential    U = -W = -qEd   Electric Potential (V)  Potential given in volts (joules/coulomb)  1V = 1 J/C

Potential Difference   V = V f - V i =  U/q  The potential differences between two points is the difference in electrical potential energy between the two points per unit charge   For any given point with potential V   Potential is the potential energy per unit charge  Compare to E = F/q and F = qE

Potential Confusion   Potential energy depends on the test charge, potential does not   The symbol for potential is the same as its unit  e.g.

Signs  As a positive charge moves along the electric field, the particle gains kinetic energy and the field loses potential and potential energy   The potential energy lost by the field goes into work    U + W = 0 or -  U = W  An electric field will naturally move a particle along the field lines, doing positive work and resulting in a decrease in potential and potential energy 

E +  Down    field does work  Up    you do work  field “does” negative work

Potential Energy and Potential  Positive charges want to move along E field, negative against it   The “natural” movement will decrease potential energy   Positive charges move naturally from high to low potential  Negative charges move naturally from low to high potential

Work   Work done by the system is positive if it decreases the potential energy   Work done by the system is negative if it increases the potential energy   The negative work done by the system is the positive work done on the system

Today’s PAL  Consider 4 situations: + charge moves with E field, + charge moves against E field, - charge moves with E field, - charge moves against E field  For each situation:  What is the sign of the change in potential energy?  What is the sign of the potential difference (final-initial)?  What is the sign of the work done by the system?  Does this happen naturally?

Work and Potential   Positive work done by the electric force reduces potential energy (W = -  U)  W = -q(V f -V i )  If there is no potential difference there is no work done by the electric force 

Potential and Energy   As a particle moves from an initial to a final position, energy is conserved:   Since U = Vq  K f = K i + qV i -q V f   Thus if you go from high to low potential (“downhill”) the particle speeds up

Conductors   All points on the surface must be at the same potential   Since there is no field inside the conductor, the electric potential is constant inside the conductor

Equipotentials  Equipotentials lines are drawn perpendicular to the electric field   The equipotentials for a single point charge are a series of concentric circles    This would mean the same point had two values for V

Point Charges and Potential  Consider a point charge q, what is the potential for the area around it?   At infinity the potential is zero   It can be shown that:  For a single point charge

Potential Energy and Two Charges  U = k q 1 q 2 / r   Example: two positive charges brought close together have an increase in potential energy

Finding Potential   Potential is a scalar (not a vector) and so can be found by summing the magnitudes of the potentials from each charge  Total V = V 1 + V 2 + V 3 … 

Next Time  Read Ch  Homework, Ch 17: P 10, 16, 35, 46