ELECTRIC FIELDS & CHARGES

Electrostatics: Means charge at rest.

Charge: Charge is a property of a mass by which it can experience force in an electric and
magnetic field. Charge can be given by transfer of electrons from one body to another. Charge
can neither be created not destroyed. Positively charged body has deficiency of electrons,
whereas negatively charged body has excess of electrons.
Unit: Coulomb “C”
CGS Unit: Franklin (electrostatic unit- esu). Also called Stat-coulomb (smallest unit).
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1 C=3∗10 Stat Coulomb
1 Faraday (Biggest unit of charge) = 96500 C
C h arge
Current = → C h arge=Current∗Time → Dimensions : [ AT ]
Time
Neutral body: A neutral body is a body on which total charge is zero.
Example: Na atom (11 protons cancel out charge of 11 electrons)
Valance electrons are free to move in a conductor, whereas in an
insulator electrons revolve in around nucleus charge.
Like mass, electric charge is an intrinsic property of protons and
electrons.
Following points are worth noting:
1. Like charges repel each other and unlike charges attract each other.
2. Charge is transferable ( elections can be given or removed to charge a body)
3. Charge is a scalar and can be of two types positive or negative.
4. There is no Charge which does not have mass.
5. Charge is quantized. The quantum of charge is e (equal to 1.602∗10 19 C). The charge on
anybody will be some integral multiple of e, i.e. q= ± ne (n = Positive integer). Charge on
anybody can never be fraction.
(i) Apart from charge, energy, angular momentum and mass are also quantized.
The quantum of energy is hν and that of angular momentum is h/ 2π.
Quantum of mass is not known till date.
(ii) The protons and neutrons are combination of other entities called quarks,
which have charges ±1/2 e and ±1/3 e. However, isolated quarks have not been
observed. So, quantum of charge is still e.
6. During any process, the net electric charge of an isolated system remains constant
(charge is conserved). Pair production and pair annihilation are two examples of
conservation of charge.
7. Accelerated charged particle radiates energy in the form of electromagnetic waves.

⊕Q
Velocity= 0 Velocity = Constant Velocity ≠ Constant (time varying)-

⊕Q ⊕Q
( i.e. at rest) Accelerated
Produces both ⃗ E ∧⃗
B
Produces only ⃗ E ( Electric & magnetic Field) Produces both ⃗E ∧⃗B
( Electric Field) But no radiation ( Electric & magnetic Field)
and radiates energy

8. Charge is invariant (does not vary).

Special theory of Relativity: When a body moves with a speed of the order of light,
some parameters (time, mass, length, area etc.) change at high speed.

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 Massat rest
Mass=

√ v2
1− 2
c
where v= speed of object and C= speed of light

Some parameters like charge do not change with speed. They are called invariants.

Example: which of the following charges is not possible?

(i) ( A ) +3.2∗10−10 C ( B )−1.6∗10−18 C ( C ) 64∗10−20 C ( D ) 4.5∗10−19 C

−10
( A ) +3.2∗10−10 C :n= Q = 3.2∗10−19 =2∗10 9 (possible )
e 1.6∗10
−18
( B )−1.6∗10−18 C :n= Q = 1.6∗10−19 =10( possible )
e 1.6∗10
−20
( C ) 64∗10−20 C : n= Q = 64∗10 −19 =4( possible )
e 1.6∗10
−19
( D ) + 4.5∗10−19 C : n= Q = 4.5∗10−19 =2.81( Not possible )
e 1.6∗10

(ii) How many electrons are there in 1 Coulomb Charge?

Q 1 18
Q=ne → n= = =6.25∗10 electrons
e 1.6∗10−19

(iii) One metallic sphere A is given positive charge whereas another identical metallic
sphere B of exactly same mass as of A is given equal amount of negative charge.
Then
(A) Mass of A mass of B still remain equal (B) Mass of A increases
(C) Mass of B decreases (D) Mass of B increases

If a body is negatively charged electrons are transferred to it, thereby increasing the
−31
mass of negatively charged body. Hence option D. melectron=9.1∗10 kg .

(iv) Calculate total number of electrons in 18 gm of H2O

1 mole of H 2 O=18 gm
23
N A of H 2 O molecules present ∈18 gm of H 2 O=6.23∗10
−¿ ¿
−¿=10e ¿

Number of electrons∈1 molecule of H 2 O (8 O∧2 H)=8 e−¿+2 e ¿

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Number of electrons∈ N A number of H 2 Omolecules=10∗N A =6.23∗10 electrons

(v) When 1014 electrons are removed from a neutral metal sphere, then the charge on
the sphere becomes
Q=ne=1014∗( 1.6∗10−19) =1.6∗10−5=16∗10−6 C=+16 μ C

(vi) 1012 α-particles (nuclei of helium) fall per second on a neutral sphere. Calculate the
time in which the sphere gets charged by 2 mC.
4

He atom=2H , w h ere , 4=Mass no . ( no . of protons+ neutrons )∧2=no .of P∨no . of e

2
 4 ++ ¿
→ C h arge=2 e ¿
α −Particle=Double ionised Helium atom → 2H

12 12
C h argetransfer on sp h ere∈1 sec=c h arge of 10 α −Particles=2 e∗10
12 −3
C h argetransfer on sp h ere∈t sec =2 e∗10 ∗t=2 mC =2∗10 C
−3
12 −3 10 −3 7
→ 2 e ¿ 10 ∗t=2∗10 → t= −19 12
=0.625∗10 ¿ 10 =6250 Sec .
2∗1.6∗10 ¿ 10

Example: Can two like charges attract each other?

(A) Yes (B) No, it is against laws of nature
Statement: Two like point charges repel each other----------True
Two unlike point charges attract each other----True

Consider a high value point charge (+Q) and an extended body of small charge (+q).
Due to induction there will be negative charge on side
nearer to point charge and positive charge on the other
side. Due to less distance of nearer side negative charge,
the force of attraction is more compared to repulsive force
of larger distance positive charge. So, net force is
attractive.
Example: Can a charged object attract a neutral body?
Yes, similar to above case (By induction).

Example: Can a positive/negative charge attract a point size neutral body?

A positive/negative charge cannot induce charge in point size neutral body. So, no forces of
interaction and hence no attraction.

Methods of charging .
(i) Friction: Whenever two bodies are rubbed against each other, some electrons from one
body are transferred to another body. In this process, one body loses electrons and the
other body gains electrons. The object to which electrons are added acquires a negative
charge, and the object which loses electrons acquires a positive charge because of the
presence of extra protons.
Different substances can be arranged in a series in such a way that if any two of them are
rubbed against each other, then the one occurring earlier in the series acquires a positive
charge while the other occurring later acquires a negative charge.

Fur Flannel Sealing wax Glass Cotton Paper

Silk Human Body Wood Metals Rubber Resin
Amber Sulphur Ebonite Guta Parcha

Example: when a piece of polythene is rubbed with wool, a charge of -2*10-7 C is

developed on Polythene. What is the amount of mass, which is transferred to the
Polythene?
−7
Q 2∗10 20 12 12
Q=ne → n= = −19
= ∗10 =1.25∗10 electrons
e 1.6∗10 16
12 12 −31 −19
Mass of 1.25∗10 electrons=1.25∗10 ∗9.1∗10 kg=11.37∗10 kg
Understanding Conductors: Whenever a charge is given to a conductor, all charges reside on
the surface of conductor only.

(ii) Charging by conduction: Suppose we bring a neutral object in contact with a positively
charged body then some of the negatively charged electrons will get transferred from the
neutral body to the positively charged body and
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 make it carry a net positive charge. Charges re-distribute among spheres till both attain
same potential. Condition is that both should be metallic spheres of identical size.
Q1+Q 2
When contact is removed, then final charge on each sphere will be Q f =
2

Example: Four identical metallic sphere A, B, C & D have charges +10C, +6C, -20C & +5C
respectively. Find final charges on A, B, C &D when AB, BC& CD are connected one by one
and removed.
10+ 6 8+ (−20 )
A∧B= =8 → A , B=+ 8 C B∧C= =−6 → B , C=−6 C
2 2
(−6 )+ 5 Final Charge:
C∧D= =−0.5 →C , D=−0.5 C , A=+8 C , B=−6 C ,C∧D=−0.5 C
2

Example: When a body is earthed, electrons from the earth flow

into the body. This means the body is
(A) Uncharged (B) Positively charged
(Answer)
(C) Negatively Charged (D) An insulator

Example: Which of the following is correct regarding electric harge?

(i) If a body is having positive charge, i.e. shortage of electrons

(ii) If a body is having negative charge, i.e. excess of electrons
(iii) Minimum Possible charge = ± 1.6*10-19 C
(iv) Charge is quantized, i.e., Q = ± ne, where n = 1,2,3,,….
(A) Both (i) & (ii) (B) Both (ii) & (iii)
(C) (i),(ii),(iii) (D) All of these. Answer

Example: Consider a neutral conducting sphere. A positive point charge is placed outside
the sphere. Then the net charge on the sphere is:

(A) Negative and distributed uniformly over the surface of the sphere.
(B) Negative and appears only at the point on the sphere closest to the point charge.
(C) Negative and distributed non-uniformly over the surface of the sphere.
(D) Zero (Answer)

Example: Charges A & B are attracted to each other and Charges B & C are attracted to
each other. If A and C ate brought close to each other, then
Answer: They repel each other

ElectroScope: The gold leaves should be light in weight

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Applications:

1. Detect the presence of electric charge on a body.

2. Compare the magnitude of charges (less deflection-less charge and vice-versa)
3. Detect the relative amount of charges.

Drawbacks:

1. It cannot measure the amount of charge on body.

2. It cannot determine the type of charge on body.

(iii) Charging by induction: This is the process of charging a neutral body by bringing it near
a charged body but not in contact. Suppose we want to provide a net positive charge to a
neutral metal plate, then in this process, we will bring a negatively charged body near the
neutral metal plate. This will accumulate positive charges in the neutral metal plate near
the side which faces the charged body, and all the free electrons will accumulate on the
opposite side. If we connect this side of the metal plate to the earth, then all the free
electrons will move to the earth. Now, if we remove the earthing and the charged body,
the bounded positive charge will redistribute themselves in the metal plate, and it will
become positively charged.

Coulomb’s Law: The force of interaction between two point charges separated by a distance ‘r’.

q 1 q2 1 q1q2 q1q2
Fα 2
∨F= 2
=K 2
r 4 π ε0 r r

[ w h ere K =
1
4 π ε0
=9∗109 N−m2 /C ²
]
K=Proportional constant∧¿

ε 0 is permittivity of free space .

For extended objects where charge is distributed, we need to integrate.