22-2 the electric field 22-3 electric field lines 22-4 the electric field due to a point charge 22-8...

22-2 The Electric Field

22-3 Electric Field Lines

22-4 The Electric Field Due to a Point Charge

22-8 A Point Charge in an Electric Field

1436-1437 د/ عادل محمد الهاشمي المدني 1

The Electric Field

1436-1437 د/ عادل محمد الهاشمي المدني 2

How does particle 1 “know” of the presence of particle 2? That is, since the particles do not touch, how can particle 2 push on particle 1—how can there be such an action at a distance?

?

The Coulomb’s law tells us how a charged particle interacts with another charged particle.

The concept of Electric Field is introduced to explain this question. .

1436-1437 د/ عادل محمد الهاشمي المدني 3

The explanation that we shall examine here is this: Particle 2 sets up an electric field at all points in the surrounding space, even if the space is a vacuum. If we place particle 1 at any point in that space, particle 1 knows of the presence of particle 2 because it is affected by the electric field particle 2 has already set up at that point. Thus, particle 2 pushes on particle 1 not by touching it as you would push on a coffee mug by making contact. Instead, particle 2 pushes by means of the electric field it has set up.

1436-1437 د/ عادل محمد الهاشمي المدني 4

The electric field is a vector field. It consists of a distribution of vectors, one for each point in the region around a charged object.

The direction of force defines the direction of field

1436-1437 د/ عادل محمد الهاشمي المدني 5

The electric field E at any point is defined in terms of the electrostatic force F that would be exerted on a e test charge q0 placed there:

0

FE

q

SI Unit of Electric Field: newton per coulomb (N/C)

1436-1437 د/ عادل محمد الهاشمي المدني 6

Electric Field Lines

1436-1437 د/ عادل محمد الهاشمي المدني 7

In order to understand the electric filed better, we will try to visualize the electric field now.

Michael Faraday introduced the idea of electric fields in the 19th century and thought of the space around a charged body as filled with electric field lines .

The direction of the field lines indicate the direction of the electric force acting on a positive test charge.

1436-1437 د/ عادل محمد الهاشمي المدني 8

The electric field vector at any point is tangent to the field line through that point

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

A closer spacing means a larger field magnitude.

1436-1437 د/ عادل محمد الهاشمي المدني 9

q

Electric field lines extend away from positive charge (where they originate) and toward negative charge (where they terminate).

1436-1437 د/ عادل محمد الهاشمي المدني 10

1436-1437 د/ عادل محمد الهاشمي المدني 11

22-4 The Electric Field Due to a Point Charge

1436-1437 د/ عادل محمد الهاشمي المدني 12

From Coulomb’s law, the electrostatic force due to q, acting on a positive test charge q0 is:

The electric field due to a point charge q is:

The field of a positive point charge is shown on the right, in vector form.

The magnitude of the field depends only on the distance between the point charge (as the field source) and the location where the field is measured. 1436-1437 د/ عادل محمد الهاشمي المدني 13

Electric field is a vector quantity. Thus, the net, or resultant, electric field due to more than one

point charge is the superposition of the field due to each charge.

The net electric field at the position of the test charge, due to n point charges, is:

0,net 01 02 03 0nE E E E E

31 210 20 302 2 2 2

10 20 30 0

ˆ ˆ ˆ ˆr r r rnn

n

q qq qk k k kr r r r

0,net 021 0

r̂n

mm

m m

qE k

r

1436-1437 د/ عادل محمد الهاشمي المدني 14

Ex = E1x + E2x + E3x +E4x

Ey = E1y + E2y + E3y +E4y

1436-1437 د/ عادل محمد الهاشمي المدني 15

Checkpoint 1The figure here shows a proton p and an electron e onan x axis.What is the direction of the electric field due to the electron at (a) point S and(b) point R? What is the direction of the net electric field at (c) point R and (d) point S?The direction of the electric field due to the electron at:

(a) Point S?

(b) Point R?

(c) The direction of the net electric field at

(c) Point R?

(d) Point S?

RightwardLeftward

Leftward

Rightward

1436-1437 د/ عادل محمد الهاشمي المدني 16

Sample Problem

1436-1437 د/ عادل محمد الهاشمي المدني 17

Figure 22-7a shows three particles with charges q1=+2Q, q2 = -2Q, and q3=-4Q, each a distance d from the origin. What net electric field is produced at the origin?

1436-1437 د/ عادل محمد الهاشمي المدني 18

To find the magnitude of which is due to q1, we use Eq. 22-3, substituting d for r and 2Q for q and obtaining

1436-1437 د/ عادل محمد الهاشمي المدني 19

22-8 A Point Charge in an Electric Field

1436-1437 د/ عادل محمد الهاشمي المدني 20

If a particle with charge q is placed in an external electric field E, an electrostatic force F acts on the particle:

e1436-1437 د/ عادل محمد الهاشمي المدني 21

Measuring the Elementary Charge

Equation 22-28 played a role in the measurement of the elementary charge e by American physicist Robert A. Millikan in 1910–1913. When tiny oil drops are sprayed into chamber A, some of them become charged, either positively or negatively, in the process. Consider a drop that drifts downward through the small hole in plate P1 and into chamber C.

1436-1437 د/ عادل محمد الهاشمي المدني 22

Millikan discovered that the values of q were always given by

in which e turned out to be the fundamental constant we call the elementary charge

1436-1437 د/ عادل محمد الهاشمي المدني 23

Ink-jet printer. Drops shot from generator G receive a charge in charging unit C. An input signal from a computer controls the charge and thus the effect of field E on where the drop lands on the paper.

1436-1437 د/ عادل محمد الهاشمي المدني 24

Tutorial

1436-1437 د/ عادل محمد الهاشمي المدني 45

Since the charge is uniformly distributed throughout a sphere, the electric field at the surface is exactly the same as it would be if the charge were all at the center. That is, the magnitude of the field is

where q is the magnitude of the total charge and R is the sphere radius.

1436-1437 د/ عادل محمد الهاشمي المدني 46

(b) The field is normal to the surface and since the charge is positive, it points outward from the surface.

1436-1437 د/ عادل محمد الهاشمي المدني 47

1436-1437 د/ عادل محمد الهاشمي المدني 49

By symmetry we see that the contributions from the two charges q1 = q2 = +e cancel each other, and we simply use Eq. 22-3 to compute magnitude of the field due to q3 = +2e.

(a) The magnitude of the net electric field is

(b) This field points at 45.0°, counterclockwise from the x axis.

1436-1437 د/ عادل محمد الهاشمي المدني 50

1436-1437 د/ عادل محمد الهاشمي المدني 56

The magnitude of the force acting on the electron is F = eE, where E is the magnitude of the electric field at its location. The acceleration of the electron is given by Newton’s second law:

1436-1437 د/ عادل محمد الهاشمي المدني 57

Home workNo. 2, 56, and 83

1436-1437 د/ عادل محمد الهاشمي المدني 59