a field is an area or volume that has a number, representing some quantity, assigned to every...

A field is an area or volume that has a number, representing some quantity, assigned to every location.

That number can be a scalar or a vector.

A football field has numbers assigned in one dimension

Define the concept of a field

A weather map is an example of a scalar field.

Every point on the map has a scalar quantity associated with it. In this case, it’s temperature.

For example, the temperature in NP is about 75o

We can also define a field in terms of vectors.

He learned this in our school!

Vector Field Examples - Has an amount and a direction associated with each position.

Example: Earth has a Gravitational Field

• Any charge will set up an electric field around it.

•It exerts an electric force on any other charged object within the field.

•It is defined as the force per positive charge.

Don’t confuse the charge that creates the field with the charge that reacts to the field

The Electric Field (E) is a vector field

Look at phet “Charges and Fields”

All electric charges set up an electric field around themselves. To determine the direction of an electric field at any given point, a positive point charge or test charge is used.

A positive point charge is like a point or an infinitely small spot that has a single positive charge.

Convention states that when testing an electric field, always use a positive point charge, never a negative one.

Electric Fields are always tested with positive point charges.

Remember: Positive Point charges come from your Pants Pocket

+

Draw the electric field around a positive charge.

+

Electric field for a positive charge

Draw the electric field for a negative charge.

Drawing Electric Fields

1. The lines must begin on positive charges and end on negative charges, or at infinity.

2. The number of lines drawn leaving a positive charge or approaching a negative charge is proportional to the amount of charge.

3. Field lines may not cross or touch each other.

4. Field lines must meet conductors or charges perpendicular to the surface of the conductor or charge.

This implies that the vector sum has two

values---which it can’t

Less ChargeExample: 2 charges

Q

Example: Charge & Plate

This is an equipotential line. Do not worry about it for now.

Back to Earth’s Gravitational Field:

Near the surface of the Earth, Earth’s gravitational field is 9.8 N/kg downwards, toward Earth’s surface.

Do larger masses experience a larger gravitational field from Earth?

What two variables does gravitational field depend on?

FgGM

1M

2

R 2M

1

GM2

R 2

Calculation of a Gravitational Field (on

Earth 9.8 m/s2)

Mass CREATINGthe field

Mass EXPERIENCINGthe field

+

Consider a positive charge in space.

The Electric Field is used to describe the effect of this charge at some point in

space.

+

Consider a positive charge in space.

+

If a positive point charge (+1) is placed at that point, a force will be exerted on it by the original charge.

Let’s say, the force is 10 N.

10 N

+

Consider a positive charge in space.

Then we can say, whenever a charge is placed at that point, for every coulomb of charge, it will have a force of 10 N act on it.

We say the electric field at that point is 10 N per coulomb.

E = 10 N/C

+

Consider a positive charge in space.

In general, we say F = Q E

If a 3 C charge is placed there, the force on it would be 3 C x 10 N/C or 30 N.

QEF

221

d

QkQF

Qd

kQF

2

Therefore, this part of Coulomb’s Law must calculate the Electric Field

Q

Another equation for Electric Field:

According to Coulomb’s Law:

Another way to calculate electric force is this:

This charge CREATES the

field

This charge EXPERIENCES the field

The electric field produced by a point or spherical charge is given by….

2d

QkE

K = Coulomb’s Constant (9.0x109 N m2/C2)

Q = The charge producing the field. Given in Coulombs

d = The distance to the point in question

The direction of the electric field is based on the direction of force for a positive charge.

Q

.0025 C

+ 20.00 m

E 9.0109 .0025C

20.002m 2

2d

QkE

= 5.6x104 N/C

Q

What is the electric field 20.00 m to the right of a (+) 0.0025 C point charge?

E=?

1) 20.m 2) 5.0m 3) 25m 4) 40.m 5) 32m

The electric field produced by a point charge is 16 N/C at a distance of 10. m. At what distance will the field be 4.0 N/C?

The electric field produced by a point charge is 16 N/C at a distance of 10.m. At what distance will the field be 4.0 N/C?

1) 20.m 2) 5.0m 3) 25m 4) 40.m 5) 32m

E kQd 2

16NC

(9.0109 Nm 2 /C 2 )Q(10.m)2

Q 1.77810 7C

4.0N

C(9.010

9 Nm 2 /C 2 )(1.77810 7C)

d 2

d 20.m

1

2

3

4

+ -

Two charges, +Q and –Q, are located two meters apart as shown. Which vector best represents the direction of the electric field at the point above them?

Two charges, +Q and –Q, are located two meters apart as shown. Which vector best represents the direction of the electric field at the point above them?

1

2

3

4

+ -

Two charges, +Q and –Q, are located two meters apart as shown. Which vector best represents the direction of the electric field at the point above them?

+ -

0.0 m

Two charges are along the x-axis. Q1 is 3.0 m from the origin and has a charge of -12.0C. Q2 is 4.5 m from the origin and has a charge of +4.0C. (all charges are along the positive x-axis)a) Calculate the electric field 8.0 m from the origin.

+Q2 = + 4.0x10-

6C

4.5 m

-Q1 = - 12.0x10-6C

3.0 m

E = ?

8.0 m

0.0 m

+Q2 = + 4.0x10-

6C

4.5 m

-Q1 = - 12.0x10-6C

3.0 m

E = ?

8.0 m

b) What force will a - 9.0 C charge experience if it is placed 8.0 m from the origin?

0.0 m

+Q2 = + 4.0x10-

6C

4.5 m

-Q1 = - 12.0x10-6C

3.0 m

-Q3 = - 9.0x10-6C

8.0 m

E = 1381 N/C F = QE

F = (-9.0x10-6C)(1380N/C)F = 0.012 N

Two point charges, separated by 1.5cm, have charges of +2 and -4C. Suppose we determine that 10 field lines radiate out from the +2C charge. If so, what might be inferred about the -4C charge with respect to field lines?1) 20 radiate out 2) 5 radiate out 3) 20 radiate in 4) 10 radiate in 5) 5 radiate in

Two point charges, separated by 1.5cm, have charges of +2 and -4C. Suppose we determine that 10 field lines radiate out from the +2C charge. If so, what might be inferred about the -4C charge with respect to field lines?1) 20 radiate out 2) 5 radiate out 3) 20 radiate in 4) 10 radiate in 5) 5 radiate in