Electric Charge

• Under conditions (e.g., rubbing) objects

can become charged

• There are two types of charge: Positive

and Negative

• When brought near each other like

charges repel and unlike charges attract

• A charged object and a neutral object will

attract

Electric Charge

• Conductors: Excess charge is free to

move around

• Insulators: Excess charge remains in

place

Electric Force

• Generally objects are neutral. There are

an equal number of positive and negative

charges.

• There is a fundamental unit of charge

e=1.6x10-19 Coulombs. Electron has a

charge of –e. Proton has a charge of e.

• The net charge on an object is:

q = Npe – Nee = ΔN e

Dipole Field Lab

• In the next two slides, the electric field (determined by the change in

electric potential versus position) if plotted versus the inverse of the

distance from the dipole cubed.

• In the first slide, all of the data are plotted and the curvature of the

line implies that there is not a direct correlation between E and r-3 .

• In the second slide, only the furthest points are plotted and there is a

clear proportionality between E and r-3 .

Dipole E vs r-3 All Points

E vs r^-3 for all points

0

10

20

30

40

50

60

0 5000 10000 15000 20000 25000 30000 35000 40000

r^-3 (m^-3)

E (

V/m

)

E (V/m)

Dipole E vs r-3 Far Points

E vs r^-3 for furthest points only

0

1

2

3

4

5

6

0 50 100 150 200 250 300 350 400 450 500

r^-3 (m^-3)

E (

V/m

)

Series1

Linear (Series1)

Electric Field Line Representation

• Electric Field Lines are a tool for

visualizing the strength and direction of the

electric field

• They could be “traced” by following and

recording the direction of the electric force

on a “slowly” moving positive charge

• Equipotential lines are another means by

which we can visualize the field

Electric Field Line Representation

• Field or flux lines origninate on positive charges and terminate on negative charges. Number of field lines leaving a charge is proportional to the charge.

• Field lines can not cross one another

• The direction of the E field at a given location is tangent to the field line at that location

• The magnitude of the E field is proportional to the number of field lines crossing perpendicular to the surface per unit area (The “density” of field lines)

Equipotential Contours

• Equipotential Contours are lines of constant Electric Potential

• Equipotential Contours are perpendicular to Electric Field lines

• The spacing of the Equipotential Countours represents the strength of the electric field

Conductors

• In conductors, some electrons are weakly

bound to their parent atoms and able to

move throughout the material.

Consequently …

• The electric field is zero everywhere within

the conductor. Electrons move to short out

the field. [Figure, automobile]

Conductors

• The Electric Field within a conductor is

zero.

• Any net charge on an isolated conductor

conductor resides on the external surface

• The electric field just outside a charged

conductor is perpendicular to the surface.

• On irregularly shaped objects the charge

density (σ) is largest where the radius of

curvature of the surface is the smallest.

Conductors

• The electric field just outside a charged

conductor is perpendicular to the surface.

The strength of the field just outside the

conductor is E=σ/ε0. (Recall that the

change in electric field from one side of a

sheet of charge to the other is σ/ε0)

• On irregularly shaped objects the charge

density (σ) is largest where the radius of

curvature of the surface is the smallest.

(Figure)

• A conductor (lightning rod) is maintained at zero electric potential (grounded). That Atmosphere at a height above the lightning rod is maintained at a higher uniform potential and we solve for the electric potential. Contours of constant electric potential are shown (arbitrary units). Notice that the space been equipotentials is smallest above the lightning rod. Here the electric field is the greatest.

Electric Potential and Electric Potential Energy

• At the back end of a TV picture tube, a uniform electric field of 600 kN/C extends over a distance of 5.0 cm and points towards the back of the tube.

Find the potential difference between the back and front end of this region.

How much work would it take to move an ion with charge +2e from the back to the front of the field region?

What would happen to an electron released at the back of the field region?

The sketch below shows cross sections of equipotential surfaces

between two charged conductors that are shown in solid black.

Various points on the equipotential surfaces near the conductors are

labeled A, B, C, ..., I

What is the direction of the electric field at B?

A) toward A

B) toward D

C) toward C

D) into the page

E) up and out of the page

What is the magnitude of the electric field at point

A?

A) 10 V/m

B) 25 V/m

C) 30 V/m

D) 75 V/m

E) 100 V/m

A point charge gains 50 mJ of electric potential energy when

it is moved from point D to point G. Determine the

magnitude of the charge.

A) 1.0 mC

B) 1.3 mC

C) 25 mC

D) 50 mC

E) 130 mC

How much work is required to move a -1 mC charge

from B to D to C?

A) +2.0 x 10-5 J D) -4.0 x 10-5 J

B) -2.0 x 10-5 J E) zero joules

C) +4.0 x 10-5 J

At which of the labeled points will an electron have

the greatest potential energy?

A) A B) D C) G D) H E) I

• Calculate the capacitance of a parallel

plate capacitor whose plates are 20 cm x

3.0 cm and are separated by a 1.0 mm air

gap.

• What is the charge on each plate if the

plates are maintained at a potential

difference of 12 Volts?

• Determine the electric field between the

plates.

• A parallel plate capacitor is charged by

connecting it to a battery.

• The capacitor is then disconnected from

the battery.

• What happens to the charge as the

distance between the plates is increased?

• What happens to the potential difference

between the plates as the distance

between the plates is increased?

• A parallel plate capacitor is charged by

connecting it to a battery.

• The capacitor remains connected to the

battery.

• What happens to the charge as the

distance between the plates is increased?

• What happens to the potential difference

between the plates as the distance

between the plates is increased?