ELECTRIC CHARGES AND FIELDS
REVIKUMAR. R
CHAPTER ONE
CLASS XII
PGT PHYSICS
JNV KOLLAM
�CONTENTS�
Electrostatics
Electrostatics is the branch of Physics which deals with the study forces, fields, and potentials arising from static charges.
INTRODUCTION -ELECTROSTATICS
ACTIVITY USING COMB AND PAPER BITS
ACTIVITY USING PLASTIC SCALE AND PAPER BITS
Methods of charging
There are three methods:
Rubbing (charging by friction)
Rubbing (charging by friction)
Rubbing (charging by friction)
When glass rod is rubbed with silk, glass acquires positive charge and silk acquires negative charge.
When plastic is rubbed with fur, plastic acquires negative charge and fur acquires positive charge.
Electricity developed on bodies, when two suitable bodies rubbed with each other is called frictional electricity or static electricity.
Charging by friction
When we rub a glass rod with silk, some of the electrons from the rod are transferred to the silk cloth. Thus the rod gets positively charged and the silk gets negatively charged.
Similarly, when we rub a plastic rod with fur, some of the electrons from fur are transferred to the plastic rod. Thus the fur gets positively charged and the plastic rod gets negatively charged.
ELECTRON THEORY OF ELECTRIFICATION
To electrify a neutral body, we need to add or remove one kind of charge. When we say that a body is charged, we always refer to this excess charge or deficit of charge. In solids, some of the electrons, being less tightly bound in the atom, are the charges which are transferred from one body to the other. A body can thus be charged positively by losing some of its electrons. Similarly, a body can be charged negatively by gaining electrons.
Like charges repel and unlike charges attract each other.
Like charges repel while unlike charges attract each other.
ELECTROSCOPE
A simple apparatus to detect charge on a body is the gold-leaf electroscope. It consists of a vertical metal rod housed in a box, with two thin gold leaves attached to its bottom end. When a charged touches the metal knob at the top of the rod, charge flows on to the leaves and they diverge. The degree of divergence is an indicator of the amount of charge.
ELECTROSCOPE
Conductors and insulators
Some substances readily allow passage of electricity through them, others do not. Those which allow electricity to pass through them easily are called conductors. They have electric charges (electrons) that are comparatively free to move inside the material. Metals, human and animal bodies and earth are conductors. Most of the non-metals like glass, porcelain, plastic, nylon, wood offer high resistance to the passage of electricity through them. They are called insulators.
Conductors and insulators
Charging by conduction
When a charged body is brought in to contact with an uncharged conductor, charge flows from the charged body to the uncharged body.
+
+
+
+
+
+
+
+
+
+
+
+
+
The process is called induction of charge and happens almost instantly. The accumulated charges remain on the surface, as shown, till the glass rod is held near the sphere.
Charging by Induction
iii) Separate the spheres by a small distance while the glass rod is still held near sphere A, as shown in Fig. (c). The two spheres are found to be oppositely charged and attract each other.
(iv) Remove the rod. The charges on spheres rearrange themselves as shown in Fig. (d).
(v)Now, separate the spheres quite apart. The charges on them get uniformly distributed over them, as shown in Fig. (e).
In this process, the metal spheres will each be equal and oppositely charged. This is charging by induction.
How can you charge a metal sphere positively without�touching it?
As the rod is brought close to the sphere, the free electrons in the sphere move away due to repulsion and start piling up at the farther end. The near end becomes positively charged due to deficit of electrons.
Charging by Induction
Charging by Induction
�BASIC PROPERTIES OF ELECTRIC CHARGE
Additivity of charges
The total charge of an isolated system is equal to an algebraic sum of individual charges of the system.
For example, the total charge of a system containing five charges +1, +2, –3, +4 and
– 5,in some arbitrary unit, is
(+1) + (+2) + (–3) + (+4) + (–5) = –1 in the same unit.
Conservation of charge
The total charge of an isolated system is always conserved that means charge can neither be created nor be destroyed but can be transferred from one body to another.
When bodies are charged by rubbing, there is transfer of electrons from one body to the other; no new charges are either created or destroyed.
Quantisation of charge
Any charged body has a total charge ± ne where ‘n` is an integer (n =0,1,2,3………..). This experimental fact is called quantization of charge.
q = ± ne, where n is an integer and e = 1.6 × 10 -19 C
By convention, the charge on an electron is taken to be negative; therefore charge on an electron is written as –e and that on a proton as +e.
The SI unit of charge is Coulomb and is denoted by the symbol C.
1𝞵C=10 -6C
How many electrons constitute one coulomb of charge?
q = ne
q=1C e = 1.6 × 10 -19 C
n=6.25 x 1018 electrons
Why can one ignore quantisation of electric charge when dealing with macroscopic i.e., large scale charges?
At the macroscopic level, one deals with charges that are enormous compared to the magnitude of charge e. A charge of magnitude, say 1 μC, contains something like 1013 times the electronic charge. At this scale, the fact that charge can increase or decrease only in units of e. Thus, at the macroscopic level, the quantisation of charge has no practical consequence and can be ignored.
At the microscopic level, where the charges involved are of the order of a few tens or hundreds of e, i.e.,they can be counted and quantisation of charge cannot be ignored.
Charles Augustin de Coulomb� (1736 – 1806)
COULOMB’S LAW
r
q1
q 2
COULOMB’S LAW
Relative permittivity Or Dielectric constant ( K Or 𝟄r)
1.How does the force between two charges change if the
2.The force between two charges placed in air at a distance r apart is F. What must be the distance between two charges so that the force become
3.What is the force between two small charged spheres having charges of 2x10-7C and 3x 10-7C placed 30cm apart in the air?
Question
Coulomb’s law in vector form
Force between multiple charges�(Principle of superposition)
q1
q2
q3
q4
Principle of superposition
Principle of superposition
Total force on any charge due to number of charges is the vector sum of all the forces due to the other charges.
What is the force acting on a charge Q placed at the centroid of the triangle?
F1 = F2 = F3 = F
R =F
Net force acting on the charge at the centroid of the triangle is zero
Four point charges qA = 2 μC, qB = –5 μC, qC = 2 μC, and qD = –5 μC are located at the corners of a square ABCD of side 10 cm. What is the�force on a charge of 1 μC placed at the centre of the square?
The repulsive force between the charges at A and at the centre O is same in magnitude with the repulsive force by the corner C to the centre O, but these forces are opposite in direction. Hence, these forces will cancel each other. Similarly attractive force between charges at D and O is cancelled by the attractive force between the charges at B and O. Therefore, the net force on 1 μC at the centre is zero..
ELECTRIC FIELD
The electric field is defined as the region or space around a charge where an electric force of attraction or repulsion can be experienced.
Electric field Intensity
q
q
P
The electric field or field intensity at a point is defined as the force experienced by unit positive charge placed at that point.
Electric field intensity due to a point charge
+q r P E
+1
Consider a point P at a distance r from a point charge +q.
Electric field intensity at the point P,
Electric dipole and Electric Dipole moment
+
-
A system has two charges qA = 2.5 × 10–7 C and qB = –2.5 × 10–7 C�located at points A: (0, 0, –15 cm) and B: (0,0, +15 cm), respectively.�What are the total charge and electric dipole moment of the system?
Total charge
= 2.5 × 10–7 C –2.5 × 10–7 C�= 0
q = 2.5 × 10–7 C
2a = 15Cm + 15Cm = 30Cm
= 0.3 m
p =2a q
p =0.3 x 2.5 × 10–7
p =7.5 × 10–8 Cm
Electric field of a dipole (On axial line)
x
Electric field of a dipole (On equatorial line )
The electric field at P due to the charge +q,
E1 Can be resolved into two components E1 Cos𝞱 and E1 Sin𝞱.
r
r
x
r
E1 Cos𝞱
E2 Cos𝞱
𝞱
𝞱
𝞱
𝞱
r
r
x
r
E1 Cos𝞱
E2 Cos𝞱
𝞱
𝞱
𝞱
𝞱
r
r
x
r
E1 Cos𝞱
E2 Cos𝞱
𝞱
𝞱
𝞱
𝞱
a
Torque acting on a dipole in an electric field
-q
+q
A
B
N
+qE
- qE
2a
𝞱
𝞱
E
Consider a dipole of charge q and length 2a placed in a uniform electric field makes an angle 𝞱 with the direction of the electric field.
Torque acting on a dipole in an electric field
2a
2aSin𝞱
+
The net force acting on the dipole + qE- qE = 0
-q
+q
E
2a
Parallel
+q
-q
2a
E
Anti parallel
E
+q
- q
2a
-q
+q
E
30o
Electric field lines
Electric field lines
The electric field lines are imaginary lines drawn in such a way that the tangent to which at any point gives the direction of the electric field at that point.
Electric field lines of a single positive Charge
Electric field lines of a single negative Charge
The field lines of a single positive charge and a single negative�
The field lines of a single positive charge are radially outward while those of a single negative charge are radially inward.
Field lines around the system of two positive charges
Field lines around the system of two positive charges gives a different picture and describe the mutual repulsion between them.
Field lines around a system of a positive and negative charge (Electric dipole)
Field lines around a system of a positive and negative charge clearly shows the mutual attraction between them.
Field lines around the system of two negative charges
ELECTRIC FIELD LINES IN A UNIFORM ELECTRIC FIELD
Uniform electric field
Electric field corresponding to a negative charge is placed with in the vicinity of a metal plate
Properties of Electric field lines.
If two lines intersect at a point, it means that at the point of intersection electric field can be two directions and hence they never intersect each other.
Continuous Charge Distribution:
A system of closely spaced charges is said to form a continuous charge distribution.
If the charge is distributed over a line then the distribution is called ‘linear charge distribution’.
Linear charge density is the charge per unit length. Its SI unit is C / m.
dq
dl
+ + + + + + + + + + + +
dq
dl
or
ii) Surface Charge Density ( σ ):
or
If the charge is distributed over a surface, then the distribution is called ‘surface charge distribution’.
Surface charge density is the charge per unit area. Its SI unit is C / m2.
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
dS
dq
(iii) Volume Charge Density ( ρ ):
If the charge is distributed over a volume, then the distribution is called ‘volume charge distribution’.
Volume charge density is the charge per unit volume. Its SI unit is C / m3.
dq
dV
Electric flux (ϕ)
The electric flux is defined as the measure of total number of electric field lines passing normally through a given surface.
If the surface is perpendicular to the field, then the flux through an area ΔS is
Δϕ = E ΔS
Electric flux (ϕ)
If the normal to the surface makes an angle 𝞱 with the electric field ,
Flux through the surface
Δϕ = E ΔS Cos 𝞱
Δϕ = E . ΔS
Total Flux through a given surface
ϕ =𝞢 E . ΔS
OR
ϕ = E . S
Unit of electric flux is Nm2/C
𝞱
GAUSS’S LAW
P
APPLICATIONS OF GAUSS’S LAW�Field due to an infinitely long straight uniformly�charged wire.
Consider an infinitely long thin straight wire with uniform linear charge density λ. Let P be a point at a distance r from the straight wire. The electric field lines are radially outward. To find the electric field intensity at P, imagine a Gaussian surface of radius r and length l. The electric flux through two flat surfaces is zero because the electric field lines are radially outward and the area vector is purpendiculat to E
𝞴
𝞴
Field due to a uniformly charged thin spherical shell�(i) Field outside the shell
Consider a spherical shell of radius R with uniform surface charge density 𝞼. Let P be a point at a distance r from the center of the spherical shell. Here the electric field lines are radially outward. To find the electric field intensity at P imagine a Gaussian surface of radius r.
(ii)Field inside the shell
Variation of electric field with distance from the centre of the spherical shell
E =0
Field due to a uniformly charged infinite plane sheet
x
x
ΔS
𝞼
Field due to a uniformly charged infinite plane sheet
Consider an infinite plane sheet of charge with uniform charge density 𝞼. To find the electric field intensity at P, imagine a Gaussian cylinder of cross sectional area A normal to the plane of the sheet. Since the electric field lines are parallel to the curved surface, the flux through this surface is zero.
x
x
𝞼
ΔS
Field due to a uniformly charged infinite plane sheet
x
x
𝞼
ΔS
Electric field between two parallel plates
+𝞼
-𝞼
I
III
II
Electric field between two parallel plates