Electric Potential

Physics 102Professor Lee

CarknerLecture 12

PAL #11 Electric Field

Electric field between charge +3q and charge -1q

Ratio of lines touching 3q to lines touching -1q must be 3 to 1

At large distance away acts as net

charge of +2q

PAL #11 Electric Field To find electric field at a point between the charges:

E = “q” for the charges is e = 1.6X10-19 C,

3q = (3)(1.6X10-19) = 4.8X10-19 C 1q = (1)(1.6X10-19) = 1.6X10-19 C

Find E from the 3q charge, find E from the 1q

charge Since both fields point the same way (to the right), add

them up

The above electric field,

A) increases to the rightB) increases to the leftC) increases upD) increases down E) is uniform

Is it possible to have a zero electric field on a line connecting two positive charges?

A) Yes, at one point on the lineB) Yes, along the entire lineC) No, the electric field must always be

greater than zeroD) No, but it would be possible for two

negative chargesE) No, the electric field is only zero at

large distances

A hollow block of metal is placed in a uniform electric field pointing straight up. What is true about the field inside the block and the charge on its top surface?

A) Field inside points up, charge on top is positive

B) Field inside points down, charge on top is negative

C) Field inside points up, charge on top is zero

D) Field inside is zero, charge on top is positive

E) Field inside is zero, charge on top is zero

Electrical Force and Energy Like any other force, the electrical force

can do work:

If a force does work, the potential energy must decrease e.g.

Decrease in PE (PE) equal to the workPE = -W = -qEd

We would like to define a quantity that

tells us about the electrical energy at a point in the field that does not depend on the test charge

Potential Difference The potential difference (V) between

two points is the difference in electrical potential energy between the two points per unit charge:

V = Vf - Vi = PE/q

For any given point with potential V Potential is the potential energy per unit

charge Potential given in volts (joules/coulomb)

1V = 1 J/C

Potential Confusion

The potential and the potential energy are two different things

Potential at a point is the same no mater what kind of test charge is put there

e.g. V = 12 V (potential is equal to 12 volts)

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 Since energy must be conserved:

An electric field will naturally move a positive

particle along the field lines, doing positive work and resulting in a decrease in potential and potential energy n.b.

E+

Down field does work “

Up gain PE

field “does” negative work

For negative

particle, everything is backwards

Work We will talk of work done by the system and

work done on the system 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 = -PE)

We can also write work as

If there is no potential difference there is no work done by the electric force

Potential and Energy We can convert potential energy into kinetic

energy As a particle moves from an initial to a final

position, energy is conserved:

Since PE = Vq KEf = KEi + qVi -q Vf

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

Equipotentials cannot cross 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:V = ke q / r

For a single point charge

Potential Energy and Two Charges

Since the potential energy is just qV, for two point charges:

The electrical energy of the situation

depends on how far apart they are and their charge 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 = V1 + V2 + V3 …

Next Time

Read Ch 17.7-17.9 Homework, Ch 17: P 10, 16, 35, 46