APPLIED PHYSICS-II
Assignment 1
Chapter 1- Motion of Charged Particle in Electric & Magnetic Field
Q1. An electron is accelerated through a potential difference of 18kV in a CRT.
Calculate the kinetic energy and velocity attained by the electron.
(Ans: Kinetic energy= 2.8 X 10-15 eV, Velocity= 7.95X107 m/s)
Q2. A proton with initial velocity of 5X106 m/s, passes through a transverse
electric field of 200 V/cm. Calculate the transverse deflection in travelling a
distance of 1 meter.
(Ans: 3.83 X 10-2 m)
Q3. An electron beam is accelerated through a potential of 1000 V. An electric
field is applied at right angle to the path of beam by rectangular plates (transverse
electric field). The distance between the plates is 2.5 cm and potential difference
is 50 V. The length of plates is 5 cm while the screen is at a distance of 30 cm.
What is the displacement of the fluorescent spot?
(Hint: V= 1000 V, Vd = 50V, l=5 cm, L= 30 cm, d= 2.5 cm)
(Ans: y1=0.0248 m, y2= 1.24 m, y=1.26 m)
Q4. If a stream of electrons, each of mass ‘m’ and charge ‘q’ and velocity 3X106
m/sec is deflected by 2mm in traversing a distance of 10 cm through an E.F of
18V/cm perpendicular to their path, find e/m in Coulomb/kg.
(Ans: 2.5X1010 C/kg)
Q5. A doubly ionized helium atom of mass 6.7X10-27 kg is accelerated by a
potential of 2800 volts. What will be its radius of curvature in a uniform magnetic
field of 0.24 Wb/m2? Determine period of revolution.
(Hint: A doubly ionized He atom has charge q= 2X proton charge= 2 X 1.6 X10-19C)
(Ans: R= 4.5 cm, T= 5.48 X 10-7 sec)
Q6. An electron moving with a velocity 1.28X106 m/sec in the positive x-direction
enters a region in which a uniform electric and magnetic fields are present such
that Ex=Ey=0, Ez= 102.4 kV/m and Bx=Bz=0, By= 8X10-2 Tesla. The electron enters
the region at t=0. Determine the location of electron at t= 5X10-6 sec.
(Ans: Particle continues to travel along x-axis)
Q7. An electron beam passes through a magnetic field of 6X10-3 Wb/m2 and an
electric field of 3.6X104 V/m., both acting simultaneously.
(a) If the path of the electron remains undeviated, find the velocity of the
electrons.
(b)If electric field is removed what will be the radius of electron path?
(Ans: velocity= 6X106 m/sec, R= 5.625 X10-3m)
Assignment - 2
Chapter 2-Poynting vector and Poynting theorem
1) If the average distance between the sun and the earth is 1.5 X 1011 m and
power radiated by sun is 3.8 X 1026 Watt, show that the average solar
energy incident on the earth’s surface is 2 Cal/cm2 min.
( Hint: S = E X H = Po/ 4πr2)
2) A charge of 1500µC is distributed over a very large sheet having surface
area of 300m2. Calculate the electric field at a distance of 25cm.
(Ans. 28.24 X 104 N/C)
3) Show that in a given volume, the energy of an EM wave is equally shared
between the electric and magnetic field.
(Hint: Ue =1/2 D.E, Um =1/2 B.H)
4) A long cylinder carries a charge density (ρ) which is proportional to the
distance from the axis: ρ=kr, for some constant k. Find the electric field
inside the cylinder.
(Hint: [∫E.ds] closed=qenclosed/ε0)
5) Calculate the electric field intensity due to a spherical charge distribution
given by
ρ=ρ0 (1-R/a)
for R≤a
=0
for R>a
Where a is the radius of the sphere. Find electric field at a point outside and
inside the charge distribution. Also find the volume of R for which electric
field E is maximum.
(Ans: R=2a/3)
6) If earth receives 2 cal min-1cm-2 solar energy, what are the magnitude of
electric and magnetic field of radiation?
(Ans: E0= 1024.3 V/m, H0=2.717 Amp/m)
7) Calculate the magnitude of poynting vector at a surface of the sun. Given
that power radiated by the sun=3.8X 1026 Watt and radius of the sun = 7X
108 meter.
(Ans: 4.87 X 107 jm-2s-1)
Assignment - 3
Chapter 3- Propagation of plane EM wave in free space and conducting medium
1) Calculate the penetration depth for 2 MHz EM wave through copper. Given:
(σ = 5.8 X 107 mho/m, µ = 4π X 10-7 Henry/m).
(Ans: 46.7 µm)
2) In a plane EM wave in free space, the electric field oscillates at a frequency
of 2X 1014 Hz and amplitude 5V/m. Find (i) the wavelength of the wave and
(ii) the amplitude of oscillating magnetic field.
(Ans: λ=1.5 µm, B0=1.6 X 10-8T)
3) The plane EM wave propagating along the X-direction has a wavelength 5.0
mm. the electric field is in Y-direction and its maximum is 38 V/m. find the
time and space varying equations for the electric and magnetic fields.
(Ans: E(x,t) = k^ (38 V/m)cos[(1.26 X 103 rad/s)x + (3.77 X 103 rad/s)t]
B(x,t) = ĵ (1.26 X 10-7 T ) cos[(1.26 X 103 rad/s)x + (3.77 X 103 rad/s)t)]
4) The conduction current density in a lossy dielectric is given as, JC =
0.02sin(109 t) Amp/m2, find the displacement current density if σ = 103
mho/m, εr = 6.5 and εo = 8.854 X 10-7 H/m.
(Ans: 1.151 cos(109t) µA/m2 )
5) For silver, σ = 3.0 MS/m. Calculate the frequency at which the depth of
penetration is 1mm. [Given μr = 1]
(Ans: 106 mHz)
6) The electromagnetic wave intensity received on the surface of the earth
from the sun is found to be 1.33 kW/m2. Find the amplitude of electric field
vector associated with sunlight as received on the earth’s surface. Assume
sunlight to be monochromatic (= 6000Å)
(Ans: Eo = 1000V/m and Ho = 2.73 Amp.turn/m)
7) A plane EM wave traveling in the positive Z-direction in an unbound loss
less dielectric medium with relative permeability μr = 1 and relative
permittivity εr = 3 has an electric field intensity E= 6 V/m. Find (i) speed of
the EM waves in the given medium (ii) impedence of the medium (iii) peak
magnetic field intensity
(Ans: (i) 1.732 X 108 m/s (ii) 2.17 X 102 Ω (iii) 2.76 X 10-2 A/m )
8) The constitution parameter of aluminium are given by μr = 1 , εr = 1 and σ =
3.54 X 107 mho/m. Find the frequency for which the skin depth/penetration
depth of aluminium is 0.01mm.
(Ans. 89.96 Hz)
9) Show that for a good conductor the magnetic field lags the electric field by
450. Determine the ratio of their amplitudes.
(Hint: α+iβ=(1+i)(σµα/2)1/2 φ=tan-1α/β)
Assignment - 4
Chapter – Quantum Mechanics
1. A particle limited to the x-axis has the wave function Ψ=ax, between x=0
and x=1; Ψ=0 elsewhere. Find the expectation value<x> of the particles
position.
Ans.a²/4.
2. A typical atomic nucleus is about 5fermi in radius. Use the uncertainty
principle to place a lower limit on the energy that an electron must have if
it is to be a part of nucleus.
Ans.39Mev
3. Find the phase & group velocities of an electron whose de Broglie
wavelength is 1.2A⁰? Ans.6.07*10⁶m/s,1.48*10 ¹⁰m/s
4. The wave function of a certain particle is Ψ=A Cos²x for –π/2 <x<π/2.
(i)
Find the value of A,(ii) find the probability that the particle be found
between
x=0,
&
x=π/4.
Ans.√8/3π , 0.462.
5. Calculate de Broglie wavelength of 40kev electrons used in certain electron
microscope?
Ans. 6.15Fm
6. Find the phase &group velocities of the de Broglie waves of an electron
whose
kinetic
energy
is
250kev.
Ans 3*10⁸m/s.
7. Normalize the wave function
Ф(x) = exp(*sinαx
Ans.√[2(1+α²)/α²] exp(-
*sinαx
8. Calculate de Broglie wavelength of an electron accelerated through a
potential
difference
of
100volts.
Ans.1.228 A⁰
9. An electron has a de-Broglie wavelength of 3pm. find its kinetic energy and
phase & group velocities of its de-Broglie waves. Rest mass energy of
electron=511keV.
Ans.2.47*10⁸m/s.
10.Normalize the wave function
Ψ(x)=0
outside the box of size L
Ψ(x) = Asinkx o<x<L
When k=π/L.
Ans.√2/L *sinπx/L.