Chapter 24: Electric Potential

24-2: Electric potential energy

Coulomb’s law looks like the gravitation law. Hence, it is conservative.

What does it mean for a force or field to be conservative?

Introduction: Why will we be introducing the electrostatic potential (V) and electric potential energy (U)?

Because they are scalars!! not vectors like F and E.

The work done by the force is independent of path!

We can assign a potential energy (U) for the electric force!

U = -W

where W is the work done by the electric force field.

If we take U∞ = 0 then,

U = - W∞

The potential energy of a charge at a point is equal to the negative of the work done by the field in bringing the charge from infinity to that point.

24-3: Electric Potential (V): is the potential energy per unit charge.

V = U/q

V = U/q = -W/q

V = - W∞/q

V = Wapplied/q

or

Wapplied = q V

Note that the work you apply to a charge is the negative of the work that the field applies on the charge (when there is no change in kinetic energy). See the work energy theorem!

The units of J/C is defined to be the volt (V).

What is the electron-volt?

For electric fields we can use: N/C or V/m.

How much energy is an eV?

24-4: Equipotential surfaces (EP)

Adjacent points that have the same electric potential form and equipotential surface.

W = 0 in going from one point to another on the same EP (regardless of path).

What is EP for a spherical charge distribution?

E is always perpendicular to EP. (why?)

What is EP for a uniform field?

24-5: Calculating the potential from the field:

Solve check point 3:

sdEVVf

i

if

What is the direction of the field?

In which process to we (the agent) do most work?

What happens to the potential when we move a distance d along the electric field?

24-6: Potential due to a Point Charge:

Notice that:

1. V is a scalar (much easier to handle than a vector!)

2. V can be positive or negative!

r

q

r

qkV

04

1

With the understanding

that V∞ = 0

24-7: Potential due to a Group of Point Charges:

n

i i

i

ii r

qVV

104

1

Solve check point 4:

Rank the arrangements according to the net electric potential produced at point P due by the protons.

24-8: Potential due to an Electric Dipole:

What is r?

What is p?

What is ?

20

cos

4

1

r

pV

What is the induced dipole moment, and what relation does it has with polarization?

24-10: Calculating the field from the potential :

sVEs

Solve check point 6: What is the direction of the electric field in the three situations? Which has the greatest magnitude?

24.11: Electric Potential Energy of a System of Point Charges:

For a single charge: U = 0

The electric potential energy of a system of fixed point charges is equal to the work that must be done by an external agent to assemble the system, bringing each charge from an infinite distance.

For two charges (q1&q2) a distance r apart:

U = k q1 q2/ r (can you prove it?)

For three charges (q1, q2 and q3):

U = k q1 q2/r12 + k q1 q3/r13 + k q2 q3/r23

Solve sample problem 25-36:

(a) What is the electric potential energy of two electrons separated by 2 nm.

(b) If the separation increases, does the potential energy increase or decrease?

What about for four charges?

24.12: Potential of a Charged Isolated Conductor:

The electric potential of a charged conductor is constant.

Can you explain why?!

What happens if a conductor is placed in an electric field?

1- V = 0 in and on the conductor

2- The free charges in the conductor will redistribute itself in order to create an (internal) electric field that cancels the external (applied) field. Also, the field at the surface is perpendicular to the surface.

How can you shield an instrument (or a person!!) from an electric field?

Place it/ him inside a conductor.

So, if you see lighting, jump into the car!!

Physics can save your life (Allah Willing)