lab

• Levitating toys

Objectives

1. Calculate electric field strength.2. Draw and interpret electric field lines.3. Identify the four properties associated with a

conductor in electrostatic equilibrium.

objectives Know:

– Electric fields: Exist near charges, originate on positives and end on negatives, never cross

– Electric field intensity equations. Understand:

– Relationship between field strength, distance, force and charge

– Behavior of charges between charged plates Be able to:

– Use the electric field equation to solve for unknown variables. – Draw and recognize electric field diagrams for:

Point charges Systems of charges Parallel plates

Electric force is a field force

Gravitational force - the mass of the Earth exerted an influence, affecting other masses which were in the surrounding neighborhood.

electrical force – The charges exerts an influence over a distance affecting other charges which were in the surrounding neighborhood

The Electric Field and Gravitational Field Concept

• Similarly, a charged object creates an electric field. Other charges in that field would feel its effect in the space. Whether a charged object enters that space or not, the electric field exists.

• How can an apple reach across space and falls toward Earth?

• The massive Earth creates a Gravitational field. Other masses in that field would feel its effect in the space. Whether a massive object enters that space or not, the gravitational field exists.

g = Fg / m

E = Fe / q

Electric Field magnitude

2

2 )(

dkQ

qd

kQq

E

qFE e

• Electric field strength (E) is the force per charge ratio. The unit for electric field is N/C

• q is the test charge – in Coulombs• Fe is the force on the test charge q – in Newton• k: constant, k = 8.99 x 109 Nm9/C2

• Q: source charge – in Coulombs

• Note that there are two charges here - the source charge and the test charge. Electric field is the force per quantity of charge on the test charge.

• The electric field strength is not dependent upon the quantity of charge on the test charge.

• The electric field strength is dependent upon the quantity of charge on the source charge Q and the distance of separation d from the source charge.

e2d

kQE

An Inverse Square Law• Electric field strength is location dependent, and its

magnitude decreases as the distance from a location to the source increases. And by whatever factor the distance is changed, the electric field strength will change inversely by the square of that factor.

E

d

E = d2

k Q ∙

example• What is the magnitude of the electric force

acting on an electron located in an electric field with an intensity of 5.0 x 103 N/C?

E = 5.0 x 103 N/C q = 1.6 x 10-19 C

F =? N

E = F/q F = Eq

F = (5.0 N x 103 N/C) x (1.6 x 10-19 C)

= 8.0 x 10-16 N

example• What is the magnitude of an electrostatic

force experienced by one elementary charge at a point in an electric field where the electric field intensity is 3.0 × 103 N/C?

E = 3.0 x 103 N/C q = 1.6 x 10-19 C

F =? N

E = F/q F = Eq

F = (3.0 N x 103 N/C) x (1.6 x 10-19 C)

= 4.8 x 10-16 N

example• The diagram above represents a uniformly

charged rod. Which graph below best represents the relationship between the magnitude of the electric field intensity (E) and the distance from the rod as measured along line AB?

A B C D

example• Suppose that two equally charged spheres attract

each other with a force of -0.5 N ("-" means attractive) when placed a distance of 30. cm from each other. Determine the charge of the spheres. PSYW

Sample problem 17D• A charge q1 = +7.00 µC is at the origin, and a charge q2 = -5.00

µC is on the x-axis 0.300 m from the origin, as shown. Find the electric field strength at point P, which is on the y-axis 0.400 m from the origin.

+ -

P

q1 q2

0.400 m

0.300 m

0.500 m

E1

E2

Class work

• Page 647 - Practice 17D

Electric Field – direction• is determined by using a POSITIVE test charge

• 1 – place test charge• 2 – draw arrow in direction pushed (net effect)• 3 – this is the field direction

+ + - +

Lines are directed away from positively charged source charges and toward negatively charged source charges

Electric Field Maps

+ -

Electric Field Maps

+ +

Rules for Drawing Electric Field Patterns

1. The lines must begin on positive charges and terminate on negative charges

2. Surround more charged objects by more lines.

The electric field is greatest at locations closest to the surface of the charge and least at locations further from the surface of the charge.

3. draw the lines of force ___________________ to the surfaces of objects at the locations where the lines connect to object's surfaces.

• The electric force, and thus the electric field, is always directed perpendicular to the surface of an object. There are never any component of force parallel to the surface.

perpendicular

4. Electric field lines should _____________________.

• Every single location in space has its own electric field strength and direction associated with it; consequently, the lines representing the field cannot cross each other at any given location in space.

never cross

• Examples of electric field lines

example• The diagram shows the electric field in the vicinity of two

charged conducting spheres, A and B. What is the static electric charge on each of the conducting spheres?

1. A is negative and B is positive. 2. A is positive and B is negative. 3. Both A and B are positive. 4. Both A and B are negative.

example• Two small metallic spheres, A and B, are separated by a

distance of 4.0 × 10-1 meter, as shown. The charge on each sphere is +1.0 × 10-6 coulomb. Point P is located near the spheres. Which arrow best represents the direction of the resultant electric field at point P due to the charges on spheres A and B?

1 2 3 4

Fields between two oppositely charged parallel plates

• If the distance separating two oppositely charged parallel plates is small compared to their area, the electric field between the plates is uniform.

• The field lines are from positive plate to the negative plate.

E is constant

• Since E=F/q, the __________________________ on a charged particle everywhere inside the plates.

• A charged particle will accelerate toward the plate with the opposite charge.

• Ex: negative charge accelerates to positive plate, and positive charge accelerate to negative plate.

force is the same

─

++++++++++++++++++++++++++++++++++++++++++++++

┼

example• As an electron moves

between two charged parallel plates from point B to point A, as shown in the diagram, the force of the electric field on the electron

1. decreases 2. increases 3. remains the same

example

• In the diagram, proton p, neutron n, and electron e are located as shown between two oppositely charged plates. The magnitude of acceleration will be greatest for the

1. neutron, because it has the greatest mass 2. neutron, because it is neutral 3. electron, because it has the smallest mass 4. proton, because it is farthest from the negative plate

Electric field and conductors

• A _______________ is material which allows electrons to move relatively freely from atom to atom.

• Electrostatic equilibrium is the condition established by charged conductors in which the excess charge has optimally distanced itself so as to reduce the total amount of repulsive forces. Once a charged conductor has reached the state of electrostatic equilibrium, there is no further motion of charge about the surface.

conductor

+

+

+

+ -

-

-

-

Four properties of conductor in electric equilibrium

1. the electric field anywhere beneath the surface of a charged conductor is zero.

• This principle of shielding is commonly utilized today as we protect delicate electrical equipment by enclosing them in metal cases.

2. Any excess charge on an isolated conductor resides entirely

on the conductor’s outer surface.

3. the electric field on the surface of the conductor is directed

entirely perpendicular to the surface.

4. A forth characteristic of conducting objects at electrostatic

equilibrium is that the electric fields are strongest at

locations along the surface where the object is most

curved.

example• A metallic sphere is positively charged. The

field at the center of the sphere due to this positive charge is

1. positive 2. negative 3. zero 4. dependent on the magnitude of the charge

Millikan’s oil-drop experiment

• In 1909, Robert Millikan performed the oil-drop experiment to measure the elementary electric charge. The experiment entailed balancing the downward gravitational force with the upward electric forces on tiny charged droplets of oil suspended between two metal plates.

Fg = Fe

m g = E q∙ ∙q = mg / EFg

Fe

• Milliken measured the forces on charged oil drops in a uniform electric field.

• He found no drop with a charge less than 1.60 x 10-19 coulomb. The charges on other drops were integral multiples of this value.

• This finding demonstrated that there is a ______________ unit of charge. This elementary charge of 1.60 x 10-19 coulomb is called the charge on a single electron.

fundamental

example• What did Milliken conclude after performing his oil-

drop experiment?

1. The charge on an electron is 1.0 C. 2. The mass of an electron is 1.7 × 10-27 kg. 3. The charge on any oil drop is an integral multiple of

the charge on an electron. 4. The charge on an oil drop may have any value

larger than 1.6 × 10-19 C.

example• The diagram, which illustrates the Milliken oil drop

experiment, shows a 3.2 × 10-14-kilogram oil drop with a charge of -1.6 × 10-18 coulomb. The oil drop was in equilibrium when the upward electrical force on the drop was equal in magnitude to the gravitational force on the drop. What was the magnitude of the electric field intensity when this oil drop was in equilibrium?

E q = m g∙ ∙E(-1.6x10-18C) = 3.2x10-14kg(9.81 N/kg)

E = 1.96 x 105 N/C = 2.0 x 105 N/C

Fnet = Fe - Fg = 0

Fe = Fg

example• An object with a net charge of 4.80 × 10-6 coulomb

experiences an electrostatic force having a magnitude of 6.00 × 10-2 newtons when placed near a negatively charged metal sphere. What is the magnitude and direction of electric field strength at this location? [show all work including substitution with units]

Given: q = 4.8 x 10-6 C

F = 6.00 x 10-2 N

Unknown: E = ? N/C

Solve: E = F / q = 6.00 x 10-2 N / 4.8 x 10-6 C

E = 1.25 x 104 N/C directed toward the sphere.

lightning• Perhaps the most known

and powerful displays of electrostatics in nature is a lightning storm.

• What is the cause and mechanism associated with lightning strikes?

• How do lightning rods serve to protect buildings from the devastating affects of a lightning strike?

Static Charge Buildup in the Clouds

• The precursor of any lightning strike is the polarization of positive and negative charges within a storm cloud. The tops of the storm clouds are known to acquire an excess of positive charge and the bottom of the storm clouds acquire an excess of negative charge.

• When a thunderhead passes over the ground, electrons on Earth's outer surface are repelled by the negatively charged cloud's bottom surface. This creates an opposite charge on the Earth's surface. Buildings, trees and even people can experience a buildup of static charge as electrons are repelled by the cloud's bottom.

• The electric field between the cloud and the Earth is similar to the electric field between two oppositely charged plates.

• When the difference in negative and positive charges between ground and cloud gets large enough, a lightning bolt begins. The excess electrons on the bottom of the cloud start a journey through the conducting air to the ground at speeds up to 60 miles per second.

• As electrons travel close to the Earth, it encounters the positive charges traveling upward, when the two types of charges meet, lightning begins.

• The enormous and rapid flow of charge along this pathway between the cloud and Earth heats the surrounding air, causing it to expand violently. The expansion of the air creates a shockwave which we observe as thunder

Lightning Rods and Other Protective Measures

• Tall buildings, farm houses and other structures susceptible to lightning strikes are often equipped with lightning rods.

• the lightning rod serves to safely divert the lightning to the ground in event that the cloud discharge its lightning via a bolt.

Check Your Understanding

1. TRUE or FALSE:The presence of lightning rods on top of buildings prevents a cloud with a static charge buildup from releasing its charge to the building.

2. TRUE or FALSE:

If you place a lightning rod on top of your home but failed to ground it, then it is unlikely that your home would be struck by lightning.

Class work

• Charge conversions and electric force practice