
1.Electrostatics (1)
8
Lecture1.1

Lecture1.2

Lecture1.3

Lecture1.4

Lecture1.5

Lecture1.6

Lecture1.7

Lecture1.8


2.Electrostatics (2)
7
Lecture2.1

Lecture2.2

Lecture2.3

Lecture2.4

Lecture2.5

Lecture2.6

Lecture2.7


3.Current Electricity (1)
9
Lecture3.1

Lecture3.2

Lecture3.3

Lecture3.4

Lecture3.5

Lecture3.6

Lecture3.7

Lecture3.8

Lecture3.9


4.Current Electricity (2)
4
Lecture4.1

Lecture4.2

Lecture4.3

Lecture4.4


5.Capacitor
6
Lecture5.1

Lecture5.2

Lecture5.3

Lecture5.4

Lecture5.5

Lecture5.6


6.RC Circuits
3
Lecture6.1

Lecture6.2

Lecture6.3


7.Magnetism and Moving Charge
16
Lecture7.1

Lecture7.2

Lecture7.3

Lecture7.4

Lecture7.5

Lecture7.6

Lecture7.7

Lecture7.8

Lecture7.9

Lecture7.10

Lecture7.11

Lecture7.12

Lecture7.13

Lecture7.14

Lecture7.15

Lecture7.16


8.Magnetism and Matter
10
Lecture8.1

Lecture8.2

Lecture8.3

Lecture8.4

Lecture8.5

Lecture8.6

Lecture8.7

Lecture8.8

Lecture8.9

Lecture8.10


9.Electromagnetic Induction
14
Lecture9.1

Lecture9.2

Lecture9.3

Lecture9.4

Lecture9.5

Lecture9.6

Lecture9.7

Lecture9.8

Lecture9.9

Lecture9.10

Lecture9.11

Lecture9.12

Lecture9.13

Lecture9.14


10.Alternating Current Circuit
8
Lecture10.1

Lecture10.2

Lecture10.3

Lecture10.4

Lecture10.5

Lecture10.6

Lecture10.7

Lecture10.8


11.Electromagnetic Waves
4
Lecture11.1

Lecture11.2

Lecture11.3

Lecture11.4


12.Photoelectric Effect
5
Lecture12.1

Lecture12.2

Lecture12.3

Lecture12.4

Lecture12.5


13.Ray Optics (Part 1)
12
Lecture13.1

Lecture13.2

Lecture13.3

Lecture13.4

Lecture13.5

Lecture13.6

Lecture13.7

Lecture13.8

Lecture13.9

Lecture13.10

Lecture13.11

Lecture13.12


14.Ray Optics (Part 2)
13
Lecture14.1

Lecture14.2

Lecture14.3

Lecture14.4

Lecture14.5

Lecture14.6

Lecture14.7

Lecture14.8

Lecture14.9

Lecture14.10

Lecture14.11

Lecture14.12

Lecture14.13


15.Ray Optics (Part 3)
6
Lecture15.1

Lecture15.2

Lecture15.3

Lecture15.4

Lecture15.5

Lecture15.6


16.Wave Optics
21
Lecture16.1

Lecture16.2

Lecture16.3

Lecture16.4

Lecture16.5

Lecture16.6

Lecture16.7

Lecture16.8

Lecture16.9

Lecture16.10

Lecture16.11

Lecture16.12

Lecture16.13

Lecture16.14

Lecture16.15

Lecture16.16

Lecture16.17

Lecture16.18

Lecture16.19

Lecture16.20

Lecture16.21


17.Atomic Structure
6
Lecture17.1

Lecture17.2

Lecture17.3

Lecture17.4

Lecture17.5

Lecture17.6


18.Nucleus
6
Lecture18.1

Lecture18.2

Lecture18.3

Lecture18.4

Lecture18.5

Lecture18.6


19.XRay
4
Lecture19.1

Lecture19.2

Lecture19.3

Lecture19.4


20.Error and Measurement
2
Lecture20.1

Lecture20.2


21.Semiconductors
9
Lecture21.1

Lecture21.2

Lecture21.3

Lecture21.4

Lecture21.5

Lecture21.6

Lecture21.7

Lecture21.8

Lecture21.9


22.Communication Systems
5
Lecture22.1

Lecture22.2

Lecture22.3

Lecture22.4

Lecture22.5

Chapter Notes – Current Electricity
The motion or dynamics of charges gives rise to new effects, which we shall study in this Chapter. Charges in motion makes an electric current.
Time rate of flow of charge through a crosssection is called electric current. Suppose, a charge Δq passes through a given cross section or area in a short time Δt, then the electric current is
I=ΔqΔt
More precisely, the instantaneous current at a given time t is
I=limΔt→0ΔqΔt=dqdt
If the current is steady (i.e., it does not change with time), then the charge q flowing through is just proportional to time t, and we have
I=qt (for steady current)
The SI unit of current is ‘ampere’ [A]. It is one of the base SI units. One ‘ampere’ is defined on the basis of the force produced by the current carrying conductors on each other, as we shall see in the next Chapter.
The system of units is such that one ampere is equal to one coulomb per second, 1A=1C1s
Electric current being one of the base or fundamental quantities in SI units,
Dimension of current = [A]
Conventional Direction of Current
Conventionally, the direction of current is taken to be the direction of flow of positive charge, (i.e., the direction of the field).In a conductor (such as copper, aluminum, etc.) the current flows due to the motion of free electrons (negatively charged particles). Hence, the direction of electric current is opposite to the direction of flow of electrons.
Current in Different Situations
(a) Due to Translatory Motion of Charges
(i) If n particles, each having a charge q, pass through a given area in time t, the current is given by
I=ΔQΔt=nqt
(ii) If n particles, each having a charge q, pass per second per unit area, the current associated with crosssectional area S is
I=ΔQΔt=nqS
(iii) If there are n particles per unit volume, each having a charge q and moving with velocity v, the current through crosssectional area S is
I=ΔQΔt=nqSΔxΔt=nqvS
(b) Due to Rotatory Motion of Charge
If a point charge q is moving in a circle of radius r with speed v, then its time period T=(2πr/v).
So through a given crosssection (perpendicular to motion), the current is
I=qt=qT=qv2πr
Application 1
The current in a wire varies with time according to the relation i = a + bt^{2}, where current i is in ampere and time t is in second_{; }a = 4A, b = 2 As^{2}.
(a) How many coulomb pass a crosssection of the wire in the time interval between t = 5 s and t = 10 s ?
(b) What constant current could transport the same charge in same time interval ?
Solution:
(a) Δq=∫510idt=∫510(4+2t2)dt
∣∣4t+23t3∣∣105=4(10−5)+23(1000−125) C
(b) Ie=ΔqΔt=603.3310−5=120.67 A
Application 2
In the Bohr model of hydrogen atom, the electron is pictured to rotate in a circular orbit of radius 5 x 10^{11 }m, at a speed of 2.2 x 10^{6} m/s. What is the current associated with electron motion ?
Solution:
The time taken to complete one rotation is
T=2πrv
Therefore, the current is
I=qt=eT=ev2πr=1.6×10−19×2.2×1062×3.14×5×10−11=1.12 mA
Current Density (J¯)
Electric current may be distributed nonuniformly over the surface through which it passes. Hence, in order to characterize the current in greater detail, we introduce the concept of current density vector J¯ at a point, defined as follows :
(1) The magnitude of J¯ is equal to the current per unit area surrounding that point and normal to the direction of charge flow. Thus,
J=dIdS
(2) The direction of J¯ is the same as the direction of velocity vector v¯ of the ordered motion of positive chargecarriers.
If the current is due to the motion of both positive and negative charges, the current density is given by
J¯=ρ+u⃗ ++ρ−u⃗ −
where ρ+ _{ }and ρ− are volume densities of positive and negative charge carriers, respectively, and u⃗ + and u⃗ − are their velocities.
In conductors, the charge is carried only by electrons. Therefore,
J¯=ρ−u⃗ −
Here, the value of ρ− is negative. Hence the directions of J¯ and u⃗ − are opposite to each other.
If at point P current ΔI passes normally through area Δs as shown. Current density J¯ at P is given by
J⃗ =limΔs→0ΔIΔSn⃗ or J⃗ =dIdsn⃗
In general, if the crosssectional area is not normal to the current, the crosssectional area normal to current will be dS cos q and so in this situation,
J=dIdScosθ
dI=JdScosθ
or dI=J⃗ .dS⃗
or I=∫J⃗ .dS⃗
Thus, the electric current is the flux of current density.
Note the following important points about current density :
(1) Both current I and current density J⃗ have directions, by definition current density J⃗ is a vector while current I is a scalar.
(2) Though the charge density ρc is defined as charge per unit volume, it may have different values at different points, as
ρc=limΔV→0ΔqΔV
(3) For uniform flow of charge through a crosssection normal to it, we have
I=nqvS
J⃗ =ISn⃗ =(nqv)n⃗ (as nv=ρc)
J⃗ =nqv⃗ =ρcv⃗
(4) For a conductor, as we shall see,
V=IR and R=ρLS
If E is the electric field, we have
V=IR
or EL=IρLS
or J=IS=1ρE or J⃗ =σE⃗
[As conductivity, σ=1resistivity,ρ ]
Thus in case of conductors, current density is proportional to electric field E⃗ . This in turn implies that
(a) Direction of current density J⃗ is same as that of electric field E⃗
(b) If electric field is uniform (i.e., E⃗ = constant) current density will be constant (as σ = constant)
(c) If electric field is zero (as in electrostatics, inside a conductor), current density and hence current will be zero.
Drift Velocity (v⃗ d)
The drift velocity is the average uniform velocity acquired by free electrons inside a metal by the application of an electric field which is responsible for current through it.
Free elecrons, under the influence of thermal agitation, move randomly throughout the metallic conductor from one point to another in an irregular manner in all possible directions as shown in Fig. (A). However, if a source of potential difference is applied across the two ends of the conductor, the electrons gain velocities tending them to move from negative to positive side of the conductor. Average value of these velocities is termed as drift velocity. The drift velocity of the electrons is no doubt superimposed on their random velocity, but in fact this is the cause for net transportation of the charge along the conductor and hence results in a current flow.In absence of any electric field [Fig.(A)], the random motion of electrons does not contribute to any current. The number of electrons crossing any plane from left to right is equal to the number of electrons crossing from right to left (otherwise metal will not remain equipotential).
When an electric field is applied, due to electric force the path of electrons in general becomes curved instead of straight lines and electrons drift opposite to the field [Fig.(B)].
Analogy with Wind
The molecules in air have random thermal velocities whose average magnitude is somewhat larger than the speed of sound (330 m/s). A pressure difference between two regions causes a net flow of molecules in one direction resulting in wind. The wind velocity (say, about 10 m/s) is much smaller than random velocity. Similarly, in a conductor, electrons have random velocities upto 10^{6} m/s. When a potential difference is applied, electrons drift with a very small velocity ( ≈10^{4} m/s) (opposite to field) resulting in current.
Current in a Conductor
Consider a conductor of uniform crosssectional area S. If n is the number of free electrons per unit volume, the charge per unit volume is ne. If v_{d} is the drift velocity, electrons move a distance v_{d} in one second. Therefore, the volume moved in one second is v_{d}S. Thus, the current,
I=chargedensity×volumetime=(ne)×(vdS)1=nevdS
⸫ J=IS=nevd or vd=Jne
Metals (conductors) have large number of free electrons per unit volume ( ≈10^{28}/m^{3}). Therefore, the drift velocity is very small ( ≈10^{4 }m/s) compared to random speed of electrons at room temperature ( ≈10^{6} m/s).
Application 3
The area of crosssection, length and density of a piece of a metal of atomic mass 60 gm/mole are 10^{6} m^{2}, 1 m and 5 x 10^{3} kg/m^{3} respectively. Find the number of free electrons per unit volume if every atom contributes one free electron. Also find the drift velocity of electrons in the metal when a current of 16 A passes through it. Given that Avogadro’s number N_{A} = 6 x 10^{23}/mole and charge on an electron e = 1.6 x 10^{19} C.
Solution:
According to Avogadro’s hypothesis,
NNA=mM so n=NV=NAmVM=NAdM (as d=mV)
⸫ n=6×1023×(5×103)(60×10−3)=5×1028 /m3
Now as each atom contributes one electron, the number of electrons per unit volume is also the same.
J=IS=1610−6=16×106 A/m2
vd=Jne=16×106(5×1028)×(1.6×10−19)=2×10−3 m/s