Chapter 16

Electric Charge and Electric Field

Objectives: The students will be able to:

• Explain the concept of electric field and determine the resultant electric field at a point some distance from two or more point charges.

• Determine the magnitude and direction of the electric force on a charged particle placed in an electric field.

16.7 The Electric Field

The electric field is the force on a small charge, divided by the charge:

(16-3)

Only need one chargeto have an electric fieldunlike Coulomb’s Law.

Region around a charge which its effect is experienced or felt.

Notice direction of the force and Efor a proton and an electron.

Electric Field

Test charge q is always positive. Therefore the direction on the force of the test charge wouldbe away from the main charge which shows direction of the electric field.

Electric Field

Test charge q is always positive. Therefore the direction on the force of the test charge wouldbe towards the main charge which shows direction of the electric field.

What are the magnitude and direction of the electric force on an electron in a uniform electric field of strength 2460N/C that points due East?

Sample Problem 1 (similar to #23 page 466)

What are the magnitude and direction of the electric force on an electron in a uniform electric field of strength 2460N/C that points due East?

Sample Problem 1 (similar to #23 page 466)

Since the E electric field points east, the force on an electron would point in the opposite direction, west. (The F force on a proton would point in the same direction as the E field).

A proton is released in a uniform electric field, and it experiences an electric force of 1.86 x 10-14N toward the south. What are the magnitude and direction( north, east, south, west) of the electric field?

Sample Problem 2 (similar to #24 page 466)

A proton is released in a uniform electric field, and it experiences an electric force of 1.86 x 1014N toward the south. What are the magnitude and direction( north, east, south, west) of the electric field?

Sample Problem 2 (similar to #24 page 466)

Proton, positive charge, will always be attracted toward a negatively charged plate/point. Field lines always point from positive to negative. If it's being attracted south, negative charge must be somewhere south of it, so field must be in a southward direction.

What is the magnitude and direction of the acceleration experienced by an electron in and electric field of 600 N/C?  How does the direction of the acceleration depend on the direction of the field at that point? 

Sample Problem 3 (similar to #27 page 466)

What is the magnitude and direction of the acceleration experienced by an electron in and electric field of 600 N/C?  How does the direction of the acceleration depend on the direction of the field at that point? 

First, looking at the given information, we know we can find Force using E = F/q. From there, you can easily find the acceleration using F = ma.

Given info:E = 600 N/Cq = 1.602e-19E = F/q600 N/C = F/(1.602e-19)F = 9.612e-17 NF = ma9.612e-17 N = (9.11e-31)aa = 1.055e14 m/s/sBecause it's an electron, it has a negative charge. This means that the electron should

always accelerate in the opposite direction of the E. Field.

Sample Problem 3 (similar to #27 page 466)

Page 466Problems 25, 27, and 30

Homework

Objectives: The students will be able to:

Explain the concept of electric field and determine the resultant electric field at a point some distance from two or more point charges.

Determine the magnitude and direction of the electric force on a charged particle placed in an electric field.

Sketch the electric field pattern in the region between charged objects.

16.7 The Electric Field

For a point charge:

(16-4a)

(16-4b)

How to derive the equation

16.7 The Electric Field

Force on a point charge in an electric field:

(16-5)

Superposition principle for electric fields:

16.7 The Electric Field

Problem solving in electrostatics: electric forces and electric fields

1. Draw a diagram; show all charges, with signs, and electric fields and forces with directions

2. Calculate forces using Coulomb’s law

3. Add forces vectorially to get result

• What is the magnitude and direction of the electric field 30.0 cm directly above a 33.0 x 10-6 C charge?

Sample Problem 1

• What is the magnitude and direction of the electric field 30.0 cm directly above a 33.0 x 10-6 C charge?

• Now, we're into point charges. In the info given, we have a radius (distance between charge and point charge), as well as 1 Charge (33e-6 C).

• E = kq/r2

• E = (8.988e9)(33e-6)/(.3)2

• E = 3.29e6 Up

• Because this charge is positive, the electric field is always away from the charge. If the point is directly above the charge, then the electric field will travel out to the point, and past it... up.

Sample Problem 1

Two point charges are separated by the distance of 10.0cm. One has a charge of -25μC (microCoulomb) and the other +50μC (microCoulomb). a.) Determine the direction and the magnitude of the electric field at point P between the two charges that is 2.0 cm from the negative charge. b.) If an electron (mass = 9.11 x 10 to -31 power kg) is placed at the rest at P and then released, what will be its initial acceleration (direction & magnitude) ?

Sample Problem 2 example 16-8 page 452

Two point charges are separated by the distance of 10.0cm. One has a charge of -25μC (micrometer) and the other +50μC (micrometer). a.) Determine the direction and the magnitude of the electric field at point P between the two charges that is 2.0 cm from the negative charge.

Sample Problem 2 example 16-8 page 452

b.) If an electron (mass = 9.11 x 10 to -11 power kg) is placed at the rest at P and then released, what will be its initial acceleration (direction & magnitude) ?

Sample Problem 2 example 16-8 page 452

The force on the electron = qE= 1.6x10-19 x 6.33x108

= 1.01x10-10 NBecause the electron is negative, the direction is opposite to the field's direction (away from the negative charge and towards the positive charge). It will feel a force to the right.

Since F=ma, a = F/ma = 1.01x10-10 / (9.11x10-31)= 1.11x1020 m/s²The direction is the same as the force, away from the negative charge and towards the positive charge which will be to the right.

16.8 Field Lines

The electric field can be represented by field lines. These lines start on a positive charge and end on a negative charge.

16.8 Field Lines

The number of field lines starting (ending) on a positive (negative) charge is proportional to the magnitude of the charge.

The electric field is stronger where the field lines are closer together.

16.8 Field Lines

Electric dipole: two equal charges, opposite in sign:

Electric Field Lines—Physical Meaning

Electric Field Lines—Examples

Beginning with positive charge and ending at negative or infinity

Drawing the electric field

Electric fields and electric force

On the Earth’s surface, the gravitational field creates 9.8 N of force on each kilogram of mass.

With gravity, the strength of the field is in newtons per kilogram (N/kg) because the field describes the amount of force per kilogram of mass.

Electric fields and electric force

With the electric field, the strength is in newtons per coulomb (N/C).

The electric field describes the amount of force per coulomb of charge.

GT stopped here.

16.8 Field Lines

The electric field between two closely spaced, oppositely charged parallel plates is constant.

Capacitors

• A capacitor is a storage device for electric charge.

Capacitors can be connected in series or parallel in circuits, just like resistors.

Capacitors

• A capacitor can be charged by connecting it to a battery or any other source of current.

• A capacitor can be discharged by connecting it to any closed circuit that allows current to flow.

How a capacitor works inside

• The simplest type of capacitor is called a parallel plate capacitor.

• It is made of two conductive metal plates that are close together, with an insulating plate in between to keep the charges from coming together.

• Wires conduct charges coming in and out of the capacitor.

How a capacitor works inside

The amount of charge a capacitor can store depends on several factors:

1. The voltage applied to the capacitor.

2. The insulating ability of the material between the positive and negative plates.

3. The area of the two plates (larger areas can hold more charge).

4. The separation distance between the plates.

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

Electric Field Lines—Examples

-

How Capacitors Store Electrical Energy

16.8 Field Lines

Summary of field lines:

1. Field lines indicate the direction of the field; the field is tangent to the line.

2. The magnitude of the field is proportional to the density of the lines.

3. Field lines start on positive charges and end on negative charges; the number is proportional to the magnitude of the charge.

16.9 Electric Fields and Conductors

The static electric field inside a conductor is zero – if it were not, the charges would move.

The net charge on a conductor is on its surface.

16.9 Electric Fields and Conductors

The electric field is perpendicular to the surface of a conductor – again, if it were not, charges would move.

phET Point charges in Electrostatic fields

• Page 466

• Problems 32 and 35

• Electric Field lines hand-out

Homework