Lesson 27
(1) Root Mean Square
The emf from an AC generator has the time dependence given by
= ! !"#$%
where ! is the peak emf, ! is the angular frequency. The period is
2!
! =
!
The mean squ
Lesson 28
(1) Driven RLC Circuit
In a series RLC circuit with an AC power source, the circuit
equation
! + ! + ! = ! !"#$
gives rise to the phasor diagram in which the current
!
!
I is in common to all
Lesson 25
(1) Mutual Induction
Imagine two wire loops near-by labeled 1 and 2. Loop 1 carries current ! which is
changing in time. The magnetic flux it creates through loop 2 is also changing, and
creates an
Lesson 30
(1) Wave Equation
Consider a stretched string on the x-axis, occupying the interval between x=0 and
x=L. The tension in it is FT . It is allowed to vibrate on the x-y plane with small
amplitude. At
Lesson 29
(1) Displacement Current
An ambiguity exists in Amperes law when the current does not run continuously in
a loop. Recall the statement of Amperes law
! !
"
! B ! d " = 0 Iin
where I in is the curre
Lesson 26
(1) LC Circuit
The circuit shown can be used to first charge up a
capacitor through a resistor and then discharge it
through an inductor without resistance. In an LC
circuit as shown, assigning curr
Lesson 11
(1) Connection of Capacitors in Parallel
In a parallel connection of capacitors of capacitances C1
and C2 as shown,
the potential differences of the two are the same:
V1 = V2 = V
while the
Lesson 24
(1) Faradays law of electromagnetic induction
This law basically says that
A time-varying magnetic field causes the appearance of an electric field.
Take a closed curve and assign to it a d
Lesson 23
(1) Motional emf
Take a length of metallic rod and move it across a magnetic field as shown:
v
E F=evB
The free electrons in the rod also move
Lesson 19
(a) Biot-Savart Law
Magnetic fields are produced by electric currents just as electric fields are produced
by electric charges. For a small current of length d! carrying current I , the magnetic
field i
Lesson 21
(1) Circulation
Definition of Circulation: Consider a closed curve in a region where a magnetic field
is present. Assign a direction of going round the curve. Divide the curve into small
segments each
Lesson 22
(1) Microscopic magnetic moments
Motion of charged particles inside atoms gives rise to microscopic magnetic
moments. These are related to the angular
momentum of the particle.
!
!
For a particle wit
Lesson 20
(1) Magnetic field of a current carrying straight wire
A segment of a straight wire lies on the z-axis occupying the length between the
coordinates z1 and z2 and carries a current I in the positive z
Lesson 13
(1) Resistance in Series
Two resistors are connected in series if the
low potential end of one is connected to
the high potential end of the other, as
shown. The same current I will flow
through both when a potential difference
V is applied a
Lesson 18
(1) Force on a Current Loop in a Uniform Magnetic field
For an arbitrary current loop in a uniform magnetic field, the total force is
! !
! "
!
F = ! I d " ! B = I # d " ! B = 0
"
"
(
)
The loop wil
Lesson 15
(1) Linear Differential Equation of Constant Coefficients
This is the equation
dnx
d n!1 x
dx
an n + an!1 n!1 +!+ a1 + a0 x = f (t )
dt
dt
dt
where an , an!1, !a1, a0 are constants and f (t) is an arbitrary
Lesson 9
(1) Electric Potential of Uniform Surface Charge on a Circular Disk
The electric potential due to a continuous charge distribution can in principle be
found by integration using the potential of a
Lesson 16
(1) Basic Magnetism
A compass needle has two poles: the north seeking and the south seeking, or simply
the north and south poles. So does a bar magnet. When the bar magnet is cut in
halves, it bec
Lesson 17
(1) Gyro-motion
Since the force on a charged particle due to a magnetic field is perpendicular to its
velocity, and hence its infinitesimal displacement, the work done by this force is zero.
From the work-energy theorem, the kinetic energy is no
Lesson 12
(1) Electric Current
Imagine a piece of surface in space. If an amount of charge
!q goes through the surface in time !t , the current
through the surface is defined by
!q
I=
!t
The unit C/s
Lesson 14
(1) Ammeter and Voltmeter
Measurement of currents and voltages are made with ammeters and voltmeters. At the
heart of both is a galvanometer, which consists of a coil
in
a magnetic field that deflects when a current passes
through. To m
Lesson 10
(1) Capacitance
A pair of conductors carrying charges Q > 0 and !Q is said to form a capacitor. The
potential difference between them is denoted by
V = V+ !V!
where V+ , V! are the potentials of t
Lesson 8
(1) Conservation of Energy in the motion of a charged particle in Electric Field
The electrostatic energy of a point charge q at a point in an electric field where the
potential is V being qV , conserv
Lesson 7
(1) Definition of Electric Potential
!
Consider the electric field E created by a charge distribution. A test charge q placed
at any location experiences the force
!
!
F = qE
!
where E is evaluated a
Lesson 3
(1) Electric Field Defined
A charge distribution is any configuration of electrically charged objects. The
distribution is discrete if it consists of a number of point charges. It is continuous if
the
Lesson 5
(1) Electric Field of a Line Charge
Consider a long thin rod with a uniform distribution of charge so that the line charge
density ! (C / m ) is the same everywhere on the rod. We will calculate the
Lesson 6
(1) Electric Flux
Consider ! plane area A placed in a region where the electric field is uniform and
a
equal to E . Choose a direction perpendicular (normal) to t! plane and denote it by
he
the ! ni