The document summarizes key concepts about electric charge and electric fields:
1) It defines electrostatics as the study of electric charges in a static or steady state condition. Some key topics covered include conductors and insulators, Coulomb's Law, electric fields, and electric field lines.
2) It explains Coulomb's Law which states that the magnitude of the electric force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
3) It defines the electric field as the electric force experienced by a test charge at a point in space, divided by the test charge. The direction of the electric field is the same as the
Electric Charge and Electric Field LectureFroyd Wess
More: http://www.pinoybix.org
Lesson Objectives:
Static Electricity; Electric Charge and Its Conservation
Electric Charge in the Atom
Insulators and Conductors
Induced Charge; the Electroscope
Coulomb’s Law
Solving Problems Involving Coulomb’s Law and Vectors
The Electric Field
Field Lines
Electric Fields and Conductors
Gauss’s Law
Electric Forces in Molecular Biology: DNA Structure and Replication
Photocopy Machines and Computer Printers Use Electrostatics
Electric Charge and Electric Field LectureFroyd Wess
More: http://www.pinoybix.org
Lesson Objectives:
Static Electricity; Electric Charge and Its Conservation
Electric Charge in the Atom
Insulators and Conductors
Induced Charge; the Electroscope
Coulomb’s Law
Solving Problems Involving Coulomb’s Law and Vectors
The Electric Field
Field Lines
Electric Fields and Conductors
Gauss’s Law
Electric Forces in Molecular Biology: DNA Structure and Replication
Photocopy Machines and Computer Printers Use Electrostatics
This is first PPT in the electrostatics series. This PPT presents idea of charge , its various methods of production like through conduction, friction, induction. It also describes working of electroscope & concept of grounding of an insulator.
#include <iostream>
using namespace std;
const int N = 40;
void sum(int*p, int n, int d[]){
int i;
*p = 0;
for(i = 0; i < n; ++i)
{
*p = *p + d[i];
}
}
int main(void){
int i;
int accum = 0;
int data[N];
for(i = 0; i < N; ++i)
{
data[i] = i;
}
sum(&accum, N, data);
cout<<"sum is " << accum << endl;
return 0;
}#include <iostream>
using namespace std;
const int N = 40;
void sum(int*p, int n, int d[]){
int i;
*p = 0;
for(i = 0; i < n; ++i)
{
*p = *p + d[i];
}
}
int main(void){
int i;
int accum = 0;
int data[N];
for(i = 0; i < N; ++i)
{
data[i] = i;
}
sum(&accum, N, data);
cout<<"sum is " << accum << endl;
return 0;
}#include <iostream>
using namespace std;
const int N = 40;
void sum(int*p, int n, int d[]){
int i;
*p = 0;
for(i = 0; i < n; ++i)
{
*p = *p + d[i];
}
}
int main(void){
int i;
int accum = 0;
int data[N];
for(i = 0; i < N; ++i)
{
data[i] = i;
}
sum(&accum, N, data);
cout<<"sum is " << accum << endl;
return 0;
}#include <iostream>
using namespace std;
const int N = 40;
void sum(int*p, int n, int d[]){
int i;
*p = 0;
for(i = 0; i < n; ++i)
{
*p = *p + d[i];
}
}
int main(void){
int i;
int accum = 0;
int data[N];
for(i = 0; i < N; ++i)
{
data[i] = i;
}
sum(&accum, N, data);
cout<<"sum is " << accum << endl;
return 0;
}#include <iostream>
using namespace std;
const int N = 40;
void sum(int*p, int n, int d[]){
int i;
*p = 0;
for(i = 0; i < n; ++i)
{
*p = *p + d[i];
}
}
int main(void){
int i;
int accum = 0;
int data[N];
for(i = 0; i < N; ++i)
{
data[i] = i;
}
sum(&accum, N, data);
cout<<"sum is " << accum << endl;
return 0;
}#include <iostream>
using namespace std;
const int N = 40;
void sum(int*p, int n, int d[]){
int i;
*p = 0;
for(i = 0; i < n; ++i)
{
*p = *p + d[i];
}
}
int main(void){
int i;
int accum = 0;
int data[N];
for(i = 0; i < N; ++i)
{
data[i] = i;
}
sum(&accum, N, data);
cout<<"sum is " << accum << endl;
return 0;
}#include <iostream>
using namespace std;
const int N = 40;
void sum(int*p, int n, int d[]){
int i;
*p = 0;
for(i = 0; i < n; ++i)
{
*p = *p + d[i];
}
}
int main(void){
int i;
int accum = 0;
int data[N];
for(i = 0; i < N; ++i)
{
data[i] = i;
}
sum(&accum, N, data);
cout<<"sum is " << accum << endl;
return 0;
}#include <iostream>
using namespace std;
const int N = 40;
void sum(int*p, int n, int d[]){
int i;
*p = 0;
for(i = 0; i < n; ++i)
{
*p = *p + d[i];
}
}
int main(void){
int i;
int accum = 0;
int data[N];
for(i = 0; i < N; ++i)
{
data[i] = i;
}
sum(&accum, N, data);
cout<<"sum is " << accum << endl;
return 0;
}#include <iostream>
using namespace std
Electric Potential And Gradient - Fied TheoryMr. RahüL YøGi
A ppt on Electric Potential And Gradient containg all the information of Electrica Potential and Electrostatic Informatio .
Containing Information About :
Electric Potential
Potential And Gradient
Electrostatic
Electric Charge
Surface and Volume Integration
This presentation is about electric potential. As we know, electric fields are vector quantities, which define electric field properties. The electric properties of space can also be described by electric potential. Electric potential is scaler. The concept of electric potential is more important due to its advantages over electric field as it has no direction which make it simpler. Electric potential is more practical than the electric field because differences in potential. Electric potentials and electric fields are associated with each other, and either can be used to describe the electrostatic properties of space. The gravitational potential energy is meaningful only in terms of the difference in potential energy in respect of reference point. The most important fact is that the Electric potential have similar characteristics as that of gravitational potential energy.
The following presentation explain about electric charge ,its properties and methods of charging a body .the presentation also explain electrostatic force
This is first PPT in the electrostatics series. This PPT presents idea of charge , its various methods of production like through conduction, friction, induction. It also describes working of electroscope & concept of grounding of an insulator.
#include <iostream>
using namespace std;
const int N = 40;
void sum(int*p, int n, int d[]){
int i;
*p = 0;
for(i = 0; i < n; ++i)
{
*p = *p + d[i];
}
}
int main(void){
int i;
int accum = 0;
int data[N];
for(i = 0; i < N; ++i)
{
data[i] = i;
}
sum(&accum, N, data);
cout<<"sum is " << accum << endl;
return 0;
}#include <iostream>
using namespace std;
const int N = 40;
void sum(int*p, int n, int d[]){
int i;
*p = 0;
for(i = 0; i < n; ++i)
{
*p = *p + d[i];
}
}
int main(void){
int i;
int accum = 0;
int data[N];
for(i = 0; i < N; ++i)
{
data[i] = i;
}
sum(&accum, N, data);
cout<<"sum is " << accum << endl;
return 0;
}#include <iostream>
using namespace std;
const int N = 40;
void sum(int*p, int n, int d[]){
int i;
*p = 0;
for(i = 0; i < n; ++i)
{
*p = *p + d[i];
}
}
int main(void){
int i;
int accum = 0;
int data[N];
for(i = 0; i < N; ++i)
{
data[i] = i;
}
sum(&accum, N, data);
cout<<"sum is " << accum << endl;
return 0;
}#include <iostream>
using namespace std;
const int N = 40;
void sum(int*p, int n, int d[]){
int i;
*p = 0;
for(i = 0; i < n; ++i)
{
*p = *p + d[i];
}
}
int main(void){
int i;
int accum = 0;
int data[N];
for(i = 0; i < N; ++i)
{
data[i] = i;
}
sum(&accum, N, data);
cout<<"sum is " << accum << endl;
return 0;
}#include <iostream>
using namespace std;
const int N = 40;
void sum(int*p, int n, int d[]){
int i;
*p = 0;
for(i = 0; i < n; ++i)
{
*p = *p + d[i];
}
}
int main(void){
int i;
int accum = 0;
int data[N];
for(i = 0; i < N; ++i)
{
data[i] = i;
}
sum(&accum, N, data);
cout<<"sum is " << accum << endl;
return 0;
}#include <iostream>
using namespace std;
const int N = 40;
void sum(int*p, int n, int d[]){
int i;
*p = 0;
for(i = 0; i < n; ++i)
{
*p = *p + d[i];
}
}
int main(void){
int i;
int accum = 0;
int data[N];
for(i = 0; i < N; ++i)
{
data[i] = i;
}
sum(&accum, N, data);
cout<<"sum is " << accum << endl;
return 0;
}#include <iostream>
using namespace std;
const int N = 40;
void sum(int*p, int n, int d[]){
int i;
*p = 0;
for(i = 0; i < n; ++i)
{
*p = *p + d[i];
}
}
int main(void){
int i;
int accum = 0;
int data[N];
for(i = 0; i < N; ++i)
{
data[i] = i;
}
sum(&accum, N, data);
cout<<"sum is " << accum << endl;
return 0;
}#include <iostream>
using namespace std;
const int N = 40;
void sum(int*p, int n, int d[]){
int i;
*p = 0;
for(i = 0; i < n; ++i)
{
*p = *p + d[i];
}
}
int main(void){
int i;
int accum = 0;
int data[N];
for(i = 0; i < N; ++i)
{
data[i] = i;
}
sum(&accum, N, data);
cout<<"sum is " << accum << endl;
return 0;
}#include <iostream>
using namespace std
Electric Potential And Gradient - Fied TheoryMr. RahüL YøGi
A ppt on Electric Potential And Gradient containg all the information of Electrica Potential and Electrostatic Informatio .
Containing Information About :
Electric Potential
Potential And Gradient
Electrostatic
Electric Charge
Surface and Volume Integration
This presentation is about electric potential. As we know, electric fields are vector quantities, which define electric field properties. The electric properties of space can also be described by electric potential. Electric potential is scaler. The concept of electric potential is more important due to its advantages over electric field as it has no direction which make it simpler. Electric potential is more practical than the electric field because differences in potential. Electric potentials and electric fields are associated with each other, and either can be used to describe the electrostatic properties of space. The gravitational potential energy is meaningful only in terms of the difference in potential energy in respect of reference point. The most important fact is that the Electric potential have similar characteristics as that of gravitational potential energy.
The following presentation explain about electric charge ,its properties and methods of charging a body .the presentation also explain electrostatic force
COMPARING ELECTROSTATIC AND GRAVITATIONAL FORCES.
Electrostatic forces gravitational force. Electrostatic is the force of attraction or repulsion between two charges at rest while the gravitational force is the force of attraction between two bodies by virtue of their masses. masses.
https://bdslearningapp.blogspot.com/2020/09/electric-charges-and-fields_10.html
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
How to Split Bills in the Odoo 17 POS ModuleCeline George
Bills have a main role in point of sale procedure. It will help to track sales, handling payments and giving receipts to customers. Bill splitting also has an important role in POS. For example, If some friends come together for dinner and if they want to divide the bill then it is possible by POS bill splitting. This slide will show how to split bills in odoo 17 POS.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
The Indian economy is classified into different sectors to simplify the analysis and understanding of economic activities. For Class 10, it's essential to grasp the sectors of the Indian economy, understand their characteristics, and recognize their importance. This guide will provide detailed notes on the Sectors of the Indian Economy Class 10, using specific long-tail keywords to enhance comprehension.
For more information, visit-www.vavaclasses.com
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
1. CHAPTER 1:
ELECTRIC CHARGE AND ELECTRIC FIELDS
i) Electrostatic
ii) conductors and insulators
iii) Coulomb’s Law
iv) Electric Fields
v) Electric Fields Calculation
vi) Electric Field Lines
vii) Electric Dipole
1.1 Electrostatic
Electrostatic is a study on the electric charges in the
static or steady state condition. In this chapter, we will
discuss the basic and the fundamental concept of electric
charges, electric fields and their characteristics.
Plastic rods and fur are good for demonstrating
electrostatics.
Benjamin Franklin (1706-1790) suggested charges
negative and positive.
2. “Two positive charges or two negative charges repel
each other. A positive charge and a negative charge
attract each other”.
Caution: Electric attraction and repulsion
The attraction and repulsion of two charged object are
sometimes summarized as “like charges repel, and
opposite charges attract”
But keep in mind that the phase “like charge” does not
mean that the two charges are exactly identical, only that
both charges have the same algebraic sign (both positive
or both negative). “Opposite charges” mean that both
objects have an electric charge, and those charges have
different sign (one positive and the other negative).
3. 1.1.1 Electric charge and the structure of matter
The structure of atoms can be described in terms of
three particles: the negatively charged electron, the
positively charged proton, and uncharged neutron (Fig
above).
Proton and neutron in an atom make up a small, very
dense core called the nucleus. (10-15 m)
Surrounding the nucleus are the electrons
(10 -10 m a far from nucleus).
4. The negative charge of the electron has exactly the
magnitude as the positive charge of proton.
1.1.2 Electric Charge is Conserved
Principle of conservation charge:
i) The algebraic sum of all electric charges in any
closed system is constant
ii) The magnitude of charge of the electron or
proton is a natural unit of charge.
In any charging process, charge is not created or
destroyed: it is merely transferred from one body to
another.
“The electric charge is quantized. (1, 2, 3, 4…)”
5. 1.2 Conductors and Insulators
Materials that allow easy
passage of charge are called
conductors. Materials that
resist electronic flow are
called insulators.
The motion of electrons
through conducts and
about insulators allows us
to observe “opposite
charges attract” and “like
charges repel.”
Charging by induction
6. 1.3 Coulomb’s Law
Charles Augustin de Coulomb (1736-1806) studied the
interaction forces of charged particles in detail in 1784.
7. Point charges
Coulomb found that
i) The electric force is proportional to ଶ
ଶ
ii) The electric force between two point charges
depends on the quantity of charge on each body,
which we will denote by q or Q. ( positive or
negative)
+ +
- -
+ -
- +
r
iii) The forces that two point charges ଵ and ଶ exert
on each other are proportional to each charge and
therefore are proportional to the product ଵ ଶ of
the two charges
ଵ ଶ
8. Coulomb’s law state that;
The magnitude of the electric force between two point
charges is directly proportional to the product of the
charges and inversely proportional to the square of the
distance between them.
In mathematical term, the magnitude F of the force that
each of two point charge ଵ and ଶ a distance r apart
exerts on the other can be expressed as;
where k is a constant.
1.3.1 Electric Constants, k
In SI units the constant, k is where ( - epsilon
nought or opsilon zero)
ଽ ଶ ଶ
By approximation
ଽ ଶ ଶ
9. Magnitude of the charge of an electron or proton, e
ିଵଽ
One Coulomb represents the negative of the total charge
ଵ଼
of about electron.
So that, the electric force is given as
Superposition of Forces: holds for any number of
charges. We can apply Coulomb’s law to any collection of
charges.
10. Example
Two point charges ଵ and ଶ , are
separated by a distance of 3.0 cm. Find the magnitude
and direction of
(i) the electric force that ଵ exerts on ଶ , and
(ii) the electric force that ଶ exerts on ଵ .
Solution
a) This problem asks for the electric forces that two
charges exert on each other, so we will need to use
Coulomb’s law. After we convert charge to coulombs
and distance to meters, the magnitude of force that
ଵ exerts on ଶ is
ଵ ଶ
ଵଶ ଶ
ିଽ ିଽ
ଽ ଶ ିଶ
ଶ
11. Since the two charges have opposite signs, the force is
attractive; that is the force that acts on ଶ is directed
toward ଵ along the line joining the two charges.
b) Newton’s third law applies to the electric force. Even
though the charges have different magnitude, the
magnitude of the force that ଶ exerts on ଵ is the
same the magnitude of the force that ଵ exerts
on ଶ . So that
ଶଵ
Example
Two point charges are located on the positive x-axis of a
coordinate system. Charge q1 = 1.0 nC is 2.0 cm from the
origin, and charge q2 = -3.0 nC is 4.0 cm from the origin.
What is the total force exerted by these two charges on a
charge q3 = 5.0 nC located at the origin?
Solution
Find the magnitude of ଵଷ
12. ଵ ଶ
ଵଷ ଶ
ିଽ ିଽ
ଽ ଶ ିଶ
ଶ
ିସ
*(this force has a negative x-component because q3 is
repelled by q1)
Then Find the magnitude of ଶଷ
ଵ ଶ
ଶଷ ଶ
ିଽ ିଽ
ଽ ଶ ିଶ
ଶ
ିହ
*(this force has a positive x-component because q3 is
attracted by q2)
So the sum of x-component is
௫
There are no y or z- components. Thus the total force on q3 is
directed to the left, with magnitude .
13. 1.4 Electric Fields
We defined the electric field at point as the electric
force experienced by a test charge q0 at the point,
divided by the charge q0.
The direction of and is the same.
14. Electric field of a point charge
Consider we have a charge q as a point source. If we
place a small test charge q0 at the field point, P at a
distance r from the point source, the magnitude F0 of
the force is given by Coulomb’s law
ଵ ȁబ ȁ
ସగఢబ మ
so that, the magnitude of electric field, E is
ଶ
But the direction of and is the same. Then the
electric field vector is given as,
ଶ
is a vector unit in r direction.
15. Example 1: Electric-field magnitude for a point charge
What is the magnitude of electric field at a field point 2.0
m from a point charge q = 4.0 nC ?
Solution
We are given the magnitude of charge and the distance
ͳ ȁݍȁ
from the object to the field point, so by using
Ͷߨ߳Ͳ ʹݎ
we could calculate the magnitude of
ଶ
16. ିଽ
ଽ ଶ ିଶ
ଶ
Example 2: Electric Field Vector for a point charge.
A point charge q = -8.0 nC is located at the origin. Find
the electric-field vector at the field point x = 1.2 m,
y = -1.6 m?
Solution
The vector of field point P is
The distance from the charge at point source, S to the
field point, P is
ଶ ଶ ଶ ଶ
The vector unit,
17. Ԧ
ଵǤଶపƸିଵǤఫƸ
ȁ ȁ ଶǤ
Hence the electric-field vector is
ͳ ݍ
ሬԦ
ܧൌ ݎƸ
Ͷߨ߳ ݎଶ
ଽ ଶ ିଶ ሻ
െͺǤͲ ൈ ͳͲିଽ ܥ
ൌ ሺͻǤͲ ൈ ͳͲ ܰ݉ ܥ ሺͲǤଓƸ െ ͲǤͺଔƸሻ
ሺʹǤͲሻଶ
ܰ ܰ
ൌ െͳͳ ଓƸ ͳͶ ଔƸ
ܥ ܥ
Example 3: Electron in a uniform field
When the terminals of a battery are connected to two
large parallel conducting plates, the resulting charges on
ሬԦ
the plate cause an electric field ܧin the region between
the plates that is very uniform.
If the plate are horizontal and separated by 1.0 cm and
the plate are connected to 100 V battery, the magnitude
of the field is E = 1.00 x 104 N/C. Suppose the is
vertically upward,
18. a) If an electron released from rest at the upper plate,
what is its acceleration?
b) What speed does the electron acquire while
traveling 1.0 cm to lower plate?
ିଵଽ
Given electron charge is and
ିଷଵ
mass
Solution:
a) Noted that is upward but is downward because the
charge of electron is negative. Thus Fy is negative. Because
Fy is constant, the electron moves with constant
acceleration ay given by,
ସ
ିଵଽ
௬
௬ ିଷଵ
ଵହ ଶ
b) The electron starts from rest, so its motion is in the y
–direction only. We can find the electron’s speed at
any position using constant-acceleration
ଶ ଶ ଶ
formula ௬ ௬ ௬ . We have ௬
and y0 = 0 so speed ௬ when y = -1.0 cm.
݉
หݒ௬ ห ൌ ටʹܽ௬ ݕൌ ටʹ ቀെͳǤ ൈ ͳͲଵହ ቁ ሺെͳǤͲ ൈ ͳͲିଶ ݉ሻ
ݏଶ
ൌ ͷǤͻ ൈ ͳͲ ݉Ȁݏ
19. Example 4: An electron trajectory
If we launch an electron into the electric field of Example
3 with an initial horizontal velocity v0, what is the
equation of its trajectory?
Solution
The acceleration is constant and in the y-direction. Hence
we can use the kinematic equation for 2-dimensional
motion with constant acceleration.
ଵ ଶ ଵ ଶ
௫ ௫ and ௬ ௬
ଶ ଶ
We have ax=0 and ay = (-e)E /m . at t =0 , x0 =y0=0, v0x = v0
and v0y=0, hence at time t,
ଵ ଶ ଵ ா ଶ
and ௬
ଶ ଶ
Eliminating t between these equations, we get
ଶ
ଶ
20. 1.5 Electric Fields Calculation
In real situations, we encounter charge that is distributed
over space. To find the field caused by a distribution, we
imagine the distribution to be made up of many point
charges, q1,q2,q3…….qn. At any given point P, each point
charge produces its own electric field ଵ ଶ ଷ ,
so a test charge q0 placed at P experiences a force ଵ ଵ
from charge q1 and a force ଶ ଶ from charge q2 and so
on.
From the principle of superposition of forces, the total
forces that the charge distribution exerts on the q0 is the
vector sum of these individual forces,
ଵ ଶ ଷ ଵ ଶ ଷ
Then the total electric field at point P,
ଵ ଶ ଷ
21. Example 1:
Point charge q1 and q2 of +12nC and -12nC respectively,
are placed 0.10 m apart. This combination of two charges
with equal magnitude and opposite sign is called an
electric dipole. Compute the electric field caused by q1,
the field caused by q2, and total field (a) point a, (b) at
point b, and (c) at point c.
Solution
a) At point a: the electric field, ଵ caused by the
positive charge q1 and the field ଶ caused by the
negative charge q2 are both directed toward the
right. The magnitude of ଵ and ଶ are;
ͳ ȁݍଵ ȁ ଽ ଶ ିଶ ሻ
ȁͳʹ ൈ ͳͲିଽ ܥȁ
ሬሬሬሬԦ
หܧଵ ห ൌ ൌൌ ሺͻǤͲ ൈ ͳͲ ܰ݉ ܥ
Ͷߨ߳ ݎଶ ሺͲǤͲ݉ሻଶ
22. ൌ ͵ǤͲ ൈ ͳͲସ ܰȀܥ
ͳ ȁݍଶ ȁ ଽ ଶ ିଶ ሻ
ȁͳʹ ൈ ͳͲିଽ ܥȁ
ሬሬሬሬԦ
หܧଶ ห ൌ ൌൌ ሺͻǤͲ ൈ ͳͲ ܰ݉ ܥ
Ͷߨ߳ ݎଶ ሺͲǤͲͶ݉ሻଶ
ൌ Ǥͺ ൈ ͳͲସ ܰȀܥ
The component of ଵ and ଶ are;
ே
ܧଵ௫ ൌ ͵ǤͲ ൈ ͳͲସ and ܧଵ௬ ൌ Ͳ
ସே
ܧଶ௫ ൌ Ǥͺ ൈ ͳͲ and ܧଶ௬ ൌ Ͳ
Hence at point a the total electric field
ଵ ଶ has components.
Ͷܰ
௫ ଵ௫ ଶ௫ ܥ
௬ ଵ௬ ଶ௬
ସே
At point a the total field has magnitude 9.8
and is directed toward the right.
Ͷܰ
ܥ
b) At point a: the electric field, ଵ caused by the
positive charge q1 is directed toward left and the
field ଶ caused by q2 is directed toward the right.
The magnitude of ଵ and ଶ are;
ͳ ȁݍଵ ȁ ଽ ଶ ିଶ ሻ
ȁͳʹ ൈ ͳͲିଽ ܥȁ
ሬሬሬሬԦ
หܧଵ ห ൌ ൌൌ ሺͻǤͲ ൈ ͳͲ ܰ݉ ܥ
Ͷߨ߳ ݎଶ ሺͲǤͲͶ݉ሻଶ
ൌ Ǥͺ ൈ ͳͲସ ܰȀܥ
23. ͳ ȁݍଶ ȁ ଽ ଶ ିଶ ሻ
ȁͳʹ ൈ ͳͲିଽ ܥȁ
ሬሬሬሬԦ
หܧଶ ห ൌ ൌൌ ሺͻǤͲ ൈ ͳͲ ܰ݉ ܥ
Ͷߨ߳ ݎଶ ሺͲǤͳͶ݉ሻଶ
ൌ ͲǤͷͷ ൈ ͳͲସ ܰȀܥ
The component of ଵ and ଶ are
ே
ܧଵ௫ ൌ െǤͺ ൈ ͳͲସ and ܧଵ௬ ൌ Ͳ
ସ ே
ܧଶ௫ ൌ ͲǤͷͷ ൈ ͳͲ and ܧଶ௬ ൌ Ͳ
Hence at point a the total electric field
ܧ ൌ ሬሬሬሬԦ ܧଶ has components
ሬሬሬሬԦ ܧଵ ሬሬሬሬԦ
ே
ܧ௫ ൌ ܧଵ௫ ܧଶ௫ ൌ ሺെǤͺ ͲǤͷͷሻ ൈ ͳͲସ
ሬԦ
ሬԦ௬ ൌ ܧଵ௬ ܧଶ௬ ൌ Ͳ Ͳ
ܧ
ସே
At point b the total field has magnitude 6.2
and is directed toward the right.
Ͷܰ
ܥ
c) At point c, both ଵ and ଶ have same magnitude,
since this point is equidistant from both charges
and charge magnitude are the same;
ͳ ȁݍଵ ȁ
ሬሬሬሬԦ ሬሬሬሬԦ
หܧଵ ห ൌ หܧଶ ห ൌ ൌ
Ͷߨ߳ ݎଶ
ଽ ଶ ିଶ ሻ
ȁͳʹ ൈ ͳͲିଽ ܥȁ
ൌ ሺͻǤͲ ൈ ͳͲ ܰ݉ ܥ
ሺͲǤͳ͵݉ሻଶ
ൌ Ǥ͵ͻ ൈ ͳͲସ ܰȀܥ
24. The direction of ଵ and ଶ are shown in Figure.
The x-component of the both vector as the same
ே ே ହ
ܧଵ௫ ൌ ܧଶ௫ ൌ ܧଵ …‘• ߙ ൌ Ǥ͵Ͳ ൈ ͳͲଷ …‘• ߙ ൌ Ǥ͵Ͳ ൈ ͳͲଷ ቀ ቁ ൌ
ଵଷ
ே
ʹǤͶ ൈ ͳͲସ
From symmetry the y-component are equal and
opposite direction so add to zero.
ே ே
ܧ௫ ൌ ܧଵ௫ ܧଶ௫ ൌ ʹሺʹǤͶሻ ൈ ͳͲଷ ൌ ͶǤͻ ൈ ͳͲଷ
ሬԦ
ሬԦ௬ ൌ ܧଵ௬ ܧଶ௬ ൌ Ͳ
ܧ
So at point c the total electric field has magnitude
ே
ͶǤͻ ൈ ͳͲଷ and its direction toward the right.
͵ܰ
ܥ
1.6 Electric Field Lines
Electric field lines can be a big help for visualizing electric
fields and making them seem more real. An electric field
line is an imaginary line or curve drawn through a region
of space so that its tangent at any point is in the
direction of the electric field vector at that point.
25. Figure below shows some of the electric field lines in a
plane (a) a single positive charge, (b) two equal-
magnitude charges, one positive and one negative
(dipole), (c) two equal positive charges.
Diagram called Field Map.