Electric FieldsElectric Fields

Fields: Action at a distanceFields: Action at a distance

• Remember in the lab, a charged Remember in the lab, a charged balloon was able to attract small balloon was able to attract small pieces of paper without touching pieces of paper without touching them?them?

Non-contact forces:Non-contact forces:

• The electric force (and the gravitational The electric force (and the gravitational force) are force) are non-contact forcesnon-contact forces. (Can you . (Can you name some contact forces?)name some contact forces?)

• Gravity can attract objects without Gravity can attract objects without touching them.touching them.

• The electric force can attract The electric force can attract oror repel repel objects without touching them.objects without touching them.

Electric FieldElectric Field

• Two charged balloons

• How can one balloon reach across space and push a second balloon away?

• The best explanation to this question involves the concept of electric field.

The Electric FieldThe Electric Field

• There is something different about the space surrounding a charged object.

• Any other charged object that is in that space feels the effect of the charge.

• A charged object creates an electric field - an alteration of the space in the region that surrounds it.

• Other charges in that field would feel the alteration of the space.

• Whether another charged object enters that space or not, the electric field exists.

Electric FieldElectric FieldAn electric field is defined as being present An electric field is defined as being present in any region where a charged object in any region where a charged object experiences an electric force. This is a experiences an electric force. This is a fancy way of saying that the only way we fancy way of saying that the only way we can tell if a field exists is to place a test can tell if a field exists is to place a test charge at that spot and see if it feels a force. charge at that spot and see if it feels a force. (In other words, it takes one to know one.)(In other words, it takes one to know one.)

A stinky analogy….A stinky analogy….

• Anyone who has ever been near a skunk that has sprayed his foul-smelling scent has experienced a stinky field. There is something about the space surrounding a skunk that exerts an influence upon people who enter that space.

• When you get close enough, your detector (i.e., your nose) begins to detect the presence of a stinky field. As you move closer and closer to the skunk, the stinky field becomes more and more intense.

Our analogy…Our analogy…• In the same manner, an electric charge creates an electric

field - it has altered the nature of the space surrounding it. And if another charge gets near enough, that charge will sense the effect.

• An electric field is sensed by a detector charge in the same way that a nose senses the stinky field.

• The strength of the stinky field is dependent on the distance from the skunk and the amount of spray.

• Similarly, the strength of the electric field is dependent on the amount of charge that creates the field and the distance from the charge.

The Concept of a FieldThe Concept of a Field

A A fieldfield is defined as a is defined as a property of spaceproperty of space in which an in which an object experiences a object experiences a forceforce..

.PAbove earth, we say there is a Above earth, we say there is a gravitational fieldgravitational field at point at point PP..

A mass A mass mm experiences a experiences a downward downward forceforce at that point. at that point.

m

F

The The directiondirection of the field is determined by the of the field is determined by the forceforce..

The Concept of a FieldThe Concept of a Field

A A fieldfield is defined as a is defined as a property of spaceproperty of space in which an in which an object experiences a object experiences a forceforce..

.PImportant note: The field exists,

whether or not another mass is

present.

The Electric FieldThe Electric Field

1. An area of influence 1. An area of influence around a charged object.around a charged object.

2. The magnitude of the field is 2. The magnitude of the field is proportional to the amount of proportional to the amount of charge creating the field, and charge creating the field, and on the distance from the on the distance from the charge.charge.

3. Electric field is a vector 3. Electric field is a vector quantity.quantity.

E

4. The 4. The magnitudemagnitude of of EE is is given by the formula:given by the formula:

N; Units

C

FE

q

N; Units

C

FE

q

Electric Field

++++ +

+++Q

.P

r

+qF

+

Calculating the strength of an Calculating the strength of an electric field:electric field:

From Coulumb’s Law, the force on a charge q when it’s From Coulumb’s Law, the force on a charge q when it’s near another charge Q that is creating a field is:near another charge Q that is creating a field is:

The electric field The electric field EE is therefore: is therefore:

2F kQq rE

q q 2

kQE

r 2

kQE

r

2

kQqF

r

Check your understandingCheck your understanding

The electric field strength in a certain The electric field strength in a certain region of space is 15 Newtons/Coulumb.region of space is 15 Newtons/Coulumb.

What is the force experienced by a 5.0 C What is the force experienced by a 5.0 C charge placed at that point in the field?charge placed at that point in the field?

Like gravity and electric force, field strength is calculated with an inverse squareformula:

• Electric field strength is location dependent, and its magnitude decreases as the distance from a location to the source increases.

• If separation distance increases by a factor of 2, the electric field strength decreases by a factor of 4 (22). If the separation distance increases by a factor of 3, the electric field strength decreases by a factor of 9 (32).

2

kQE

r 2

kQE

r

Check your understanding:

Charge Q acts as a point charge to create an electric field. Its strength, measured a distance of 30 cm away, is 40 N/C. What is the magnitude of the electric field strength that you would expect to be measured at a distance of ...

a. 60 cm away?

b. 15 cm away?

c. 3 cm away?

The Direction of Electric FieldThe Direction of Electric Field

The The directiondirection of an electric field at any point is the of an electric field at any point is the same as the direction that a same as the direction that a positivepositive charge would charge would move move IFIF it were placed at that point. it were placed at that point.

ExampleExample What is the electric field at point What is the electric field at point PP, , a distance of a distance of 3.0 m3.0 m from a negative charge from a negative charge of of –8.0 x 10–8.0 x 10-9-9 C C??

.r

P

-Q3 m

E = ? First, find the magnitude:First, find the magnitude:2

2

9 -9NmC

2 2

(9 x 10 )(8 x 10 C)

(3 m)

kQE

r

E = 8.00 N/CE = 8.00 N/C

The direction is the same as the force on a positive The direction is the same as the force on a positive charge charge ifif it were placed at the point P: it were placed at the point P: toward –Qtoward –Q..

EE = 8.00 N, toward -Q = 8.00 N, toward -Q

Sample ProblemSample Problem• What is the electric field strength 0.30 m What is the electric field strength 0.30 m

away from Van de Graff generator with a away from Van de Graff generator with a charge of 1.2 x 10charge of 1.2 x 10-6-6 C ? C ?

• What is the force on a 0.1 x 10What is the force on a 0.1 x 10-6-6 C test C test charge at this point from .30 m away from charge at this point from .30 m away from the generator ?the generator ?

Electric Field LinesElectric Field Lines

++++ +

+++Q --

-- -

----Q

Electric Field LinesElectric Field Lines are imaginary lines drawn in are imaginary lines drawn in such a way that their direction at any point is the such a way that their direction at any point is the same as the direction of the field at that point.same as the direction of the field at that point.

BASED ON A POSTITIVE TEST CHARGE IN THE FIELDBASED ON A POSTITIVE TEST CHARGE IN THE FIELD..

Field lines go Field lines go awayaway from from positivepositive charges and charges and towardtoward negativenegative charges. charges.

Electric Field LinesElectric Field Lines

It is very important that you notice that the It is very important that you notice that the map lines have a directionmap lines have a direction to them. The to them. The direction represents the motion of the direction represents the motion of the positive test charge when placed at different positive test charge when placed at different points around the field.  You should also points around the field.  You should also notice that field lines never cross each notice that field lines never cross each other.  The closer the field lines are to each other.  The closer the field lines are to each other, the greater the field intensity or field other, the greater the field intensity or field strength.strength.

Check your understanding:Check your understanding:

True or False:True or False:

Every electric charge is surrounded by an Every electric charge is surrounded by an electric field.electric field.

Check your understanding:Check your understanding:• Draw arrows (NOT charges) on this Draw arrows (NOT charges) on this

diagram to indicate that the charge on diagram to indicate that the charge on the left is negative, and the charge on the the left is negative, and the charge on the right is positive:right is positive: