Slide 1Fig 23CO, p.707 Chapter 23: Electric Field 23-3 Coulomb’s Law 23-4 Electric Field 23-6...

Fig 23CO, p.707

Chapter 23: Electric Field

23-3 Coulomb’s Law

23-4 Electric Field

23-6 Electric field lines

23-7 Motion of charged particles in a

uniform electric field

INTRODUCTION

Fig 23-2, p.708

Fig 23-1, p.708

(a) Negatively charged rubber rod suspended by a thread is attracted to a

positively charged glass rod.

(b) (b) A negatively charged rubber rod is repelled by another negatively charged

rubber rod.

Fig 23-4, p.710

Charging a metallic object by induction (that is, the two objects never touch each other). (a) A neutral metallic sphere, with equal numbers of positive and negative charges.

(b) The electrons on the neutral sphere are redistributed when a charged rubber rod is placed near the sphere.

(c) When the sphere is grounded, some of its electrons leave through the ground wire.

(d) When the ground connection is removed, the sphere has excess positive charge that is nonuniformly distributed.

(e) When the rod is removed, the remaining electrons redistribute uniformly and there is a net uniform distribution of positive charge on the sphere.

Fig 23-5a, p.710

(a) The charged object on the left induces a charge distribution on the surface of an insulator due to realignment of charges in the molecules.

Fig 23-5b, p.710

Table 23-1, p.712

Fig 23-7, p.713

Two point charges separated by a distance r exert a force

on each other that is given by Coulomb’s law. The force F21

exerted by q2 on q1 is equal in magnitude and opposite in

direction to the force F12 exerted by q1 on q2.

(a)When the charges are of the same sign, the force is

repulsive.

(b) (b) When the charges are of opposite signs, the force is

attractive.

Fig 23-7a, p.713

Charles Coulomb French physicist (1736–1806)

Coulomb’s experiments showed that the electric

force between two stationary charged particles

• is inversely proportional to the square of the

separation r between the particles

and directed along the line joining them;

• is proportional to the product of the charges q1

and q2 on the two particles;

• is attractive if the charges are of opposite sign

and repulsive if the charges have the same sign.

The value of the Coulomb constant ke depends

on the choice of units. The SI unit of charge is

the coulomb (C). The Coulomb constant ke in SI

units has the value ke = 8.9875 x109 N.m2/C2

1 2

2

1 2

2

1

e

F q q

Fr

q qF k r

r

��

��

Using Newton’s law of gravitation

Thus, the gravitational force between charged atomic particles is negligible when compared with the electric force.

The electron and proton of a hydrogen atom are separated (on the average) by a

distance of approximately 5.3 x10-11 m. Find the magnitudes of the electric force

and the gravitational force between the two particles.

* The gravitational field g at a point in space, g = Fg / m.

* An electric field is said to exist in the region of space around a charged object. When another charged object enters this electric field, an electric force acts on it.

The vector E has the SI units of newtons per coulomb (N/C),

When a particle of charge q and mass m is placed in an electric field E, the electricforce exerted on the charge is qE. If this is the only force exerted on the particle, it must be the net force and so must cause the particle to accelerate. In this case,Newton’s second law applied to the particle gives;

Fe = qE = ma

The acceleration of the particle is therefore

a = qE/m

•If E is uniform (that is, constant in magnitude and direction), then the acceleration is constant.• If the particle has a positive charge, then its acceleration is in the direction of the electric field. •If the particle has a negative charge, then its acceleration is in the direction opposite the electric field.

A positive point charge q of mass m is released from rest in auniform electric field E directed along the x axis. Describe its motion.

we can apply the equations of kinematics in one dimension

Taking xi = 0 and vxi = o

The kinetic energy of the charge after it has moved a distance x = xf-xi, is

We can also obtain this result from the work–kinetic energy theorem because the work done by the electric force is Fex = qEx and W = ∆K

An electron enters the region of a uniform electric field with vo=3.00x106 m/s and E= 200 N/C. The horizontal length of the plates is l = 0.100 m.

(a) Find the acceleration of the electron while it isin the electric field.

(b) Find the time it takes the electron to travel through the field.

(c) What is the vertical displacement y of the electron while it is in the field?

If the separation between the plates is less than this, the electronwill strike the positive plate.

Electric charges have the following important properties:• Unlike charges attract one another, and like charges repel one another.• Charge is conserved.• Charge is quantized—that is, it exists in discrete packets that are some integralmultiple of the electronic charge.

Conductors are materials in which charges move freely. Insulators are materialsin which charges do not move freely.

where ˆr is a unit vector directed from the charge to the point in question.

The electric field is directed radially outward from a positive charge and radially inward toward a negative charge.

The electric field due to a group of point charges can be obtained by usingthe superposition principle. That is, the total electric field at some point equals the vector sum of the electric fields of all the charges:

Electric field lines describe an electric field in any region of space. The numberof lines per unit area through a surface perpendicular to the lines is proportionalto the magnitude of E in that region.

A charged particle of mass m and charge q moving in an electric field E has anacceleration

23-7; Three point charges are located at the corners of an equilateral triangle. Calculate the net electric force on the 7.00 uC charge.

23-8: Two small beads having positive charges 3q and q are fixed at the opposite ends of a horizontal insulating rod extending from the origin to the point x =d. a third small charged bead is free to slide on the rod. At what position is the third bead in equilibrium? Can it be in stable equilibrium?

Problem 23-12; An object having a net charge of 24.0 C is placed in a uniform electric field of 610 N/C that is directed vertically. What is the mass of this object if it “floats” in the field?

3-18; Two 2.00uC point charges are located on the x axis. One is at x = 1.00 m, and the other is at x =- 1.00 m. (a) Determine the electric field on the y axis at y =0.500 m. (b) Calculate the electric force on a - 3.00uC charge placed on the y axis at y = 0.500 m.

23-41; An electron and a proton are each placed at rest in an electric field of 520 N/C. Calculate the speed of each particle 48.0 ns after being released.

23-44; The electrons in a particle beam each have a kinetic energy of 1.60 x 10-

17 J. What are the magnitude and direction of the electric field that stops these electrons in a distance of 10.0 cm?

Fig 23-25, p.726

مقدارها :13-23مثال موجبة بشحنة مشحون جسم يتحرك

q وكتلتهm منتظم كهربي مجال موضح Eخالل هو كما ،

االبتدائية سرعته كانت فإذا الجسم؛ voبالرسم حركة أوصف

بسيطة خطية حركة الجسم حركة Simple Linear Motionتعتبر

F = qE = ma → a = qE/m

v = vo + at

X = vot + ½ a t2

V2 = vo2 + 2ax

x = 0 → vo = 0

x= ½ a t2 = qEt2/2m األزاحة

v=at = qEt/m & V2=2ax = 2qEx/m

K = ½ mv2 = ½ m 2qEx/m = qEx الحركية الطاقة

Fig 23-26, p.726

الجاذبية بمجال المقذوفات حركة بالرسم الموضحة الجسم حركة تكافئ

منتظم 23-7 كهربي بمجال مشحون جسيم Motion of charged حركةparticles in a

uniform electric field

F = qE = ma

هو المشحون الجسم تسارع ويكون

a= qE/m

اتجاه * وعكس الموجبة للشحنة المحال باتجاه الجسم تسارع يكونالسالبة للشحنة المجال

منتظم كهربي مجال خالل ألكترون :Eيتحرك فأن

a’= - eE/m j’

vx= v0 ثابت= & vy=at= eEt/m

x=vot & y = ½ at2 = - eEt2/2m

Fig 23-27, p.728

Figure 23.27 Schematic diagram of a cathode ray tube. Electrons leaving the

cathode C are accelerated to the anode A. In addition to accelerating

electrons, the electron gun is also used to focus the beam of electrons, and the

plates deflect the beam.

Slide 1Fig 23CO, p.707 Chapter 23: Electric Field 23-3 Coulomb’s Law 23-4 Electric Field 23-6...

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Transcript of Slide 1Fig 23CO, p.707 Chapter 23: Electric Field 23-3 Coulomb’s Law 23-4 Electric Field 23-6...