-
Answer the following questions regarding earth's magnetism:
(a) A vector needs three quantities for its
specification. Name the three independent quantities conventionally used to
specify the earth's magnetic field.
(b) The angle of dip at a location in
southern India is about
. Would you
expect a greater or smaller dip angle in Britain?
(c) If you made a map of magnetic field
lines at Melbourne in Australia, would the lines seem to go into the ground or
come out of the ground?
(d)In which direction would a compass free
to move in the vertical plane point to, if located right on the geomagnetic
north or south pole?
(e) The earth's field, it is claimed,
roughly approximates the field due to a dipole of m magnetic moment
located
at its centre. Check the order of magnitude of this number in some way.
(f) Geologists claim that besides the main
magnetic N-S poles, there are several local poles on the earth's surface
oriented in different directions. How is such a thing possible at all?
View Answer play_arrow
-
Answer the following questions
(a) The earth's
magnetic field Varies from point to point in space. Does it also change with
time? If so, on what time scale does it change appreciably?
(b) The earth?s
core is known to contain iron. Yet geologists do not regard this as a source of
the earth?s magnetism. Why?
(c)The charged
currents in the outer conducting regions of the earth?s core are thought to be
responsible for earth?s magnetism. What might be the ?battery? (i.e. the source
of energy) to sustain these currents?
(d)The earth may
have even reversed the direction of its field several times during its history
of 4 to 5 billion years. How can geologists known about the earth?s field in
such distant past?
(e)The earth?s
field departs from its dipole shape substantially at large distances (greater
than about 30,000 km). What agencies may be responsible for this distortion?
(f)Interstellar
space has an extremely weak magnetic field of the order of . Can such a weak field be of any significant consequence?
Explain.
View Answer play_arrow
-
A short bar magnet placed with its axis at
with
a uniform external magnetic field of 0.25 T experiences a torque of magnitude
equal to
. What is
the magnitude of magnetic moment of the magnet?
View Answer play_arrow
-
A short bar magnet of magnetic moment
is
placed in a uniform magnetic field of 0.15T. If the bar is free to rotate in
the plane of the field, which orientation would correspond to its (a) stable,
and (b) unstable equilibrium? What is the potential energy of the magnet in
each case?
View Answer play_arrow
-
A closely would solenoid of 800 turns and area of cross
section
carries a
current of 3.0 A. Explain the sense in which the solenoid acts like a bar
magnet. What is its associated magnetic moment?
View Answer play_arrow
-
If the solenoid in Exercise 5.5 is free to turn about the
vertical direction and a uniform horizontal magnetic field of 0.25 T is
applied, what is the magnitude of the torque on the solenoid when its axis
makes an angle of
with the
direction of the applied field?
View Answer play_arrow
-
A bar magnet of magnetic moment
lies
aligned with the direction of a uniform magnetic field of 0.22 T.
(a) What is the amount of work required by
an external torque to turn the magnet so as to align its magnetic moment, (i)
normal to the field direction, (ii) opposite to the field direction ?
(b) What is the torque on the magnet in
cases (i) and (ii)?
View Answer play_arrow
-
A closely wound solenoid of 2000 turns and area of
cross-section
, carrying
a current of 4.0 A, is suspended through its centre allowing it to turn in a
horizontal plane.
(a) What is the magnetic moment associated
with the solenoid?
(b) What is the force and torque on the
solenoid if a uniform horizontal magnetic field of
is
set up at an angle of
with the
axis of the solenoid?
View Answer play_arrow
-
A circular coil of 16 turns and radius 10 cm carrying a
current of 0.75 A rests with its plane normal to an external field of magnitude
. The coil
is free to turn about an axis in its plane perpendicular to the field
direction. When the coil is turned slightly and released, it oscillates about
its stable equilibrium with a frequency of
. What is
the moment of inertia of the coil about its axis of rotation?
View Answer play_arrow
-
A magnetic needle free to rotate in a vertical plane
parallel to the magnetic meridian has its north tip pointing down at
with the
horizontal. The horizontal component of the earth's magnetic field at the place
is known to be 0.35 G. Determine the magnitude of the earth's magnetic field at
the place.
View Answer play_arrow
-
At a certain location in Africa, a compass points
west of
the geographic north. The north tip of the magnetic needle of a dip circle
placed in the plane of magnetic meridian points
above the
horizontal. The horizontal component of the earth's field is measured to be
0.16 G. Specify the direction and magnitude of the earth's field at the
location.
View Answer play_arrow
-
A short bar magnet has a magnetic moment of
. Give the
direction and magnitude of the magnetic field produced by the magnet at a
distance of 10 cm from the centre of the magnet on (a) the axis, (b) the
equatorial lines (normal bisector) of the magnet.
View Answer play_arrow
-
A short bar magnet placed in a horizontal plane has its axis aligned along the magnetic north-south direction. Null points are found on the axis of the magnet at 14 cm from the centre of the magnet. The earth’s magnetic field at the place is 0.36 G and the angle of is zero. What is the total magnetic field the normal bisector of the magnet at the same distance as the null-points (i.e., 14 cm) from the centre of the magnet? (At null points, field due to a magnet is equal and opposite the horizontal component of earth's magnetic, field.)
View Answer play_arrow
-
If the bar magnet in Exercise 5.13 is turn around by
, where
will the new null-points be located?
View Answer play_arrow
-
A short bar magnet of magnetic moment
is
placed with its axis perpendicular to the earth's field direction. At what
distance from the centre of the magnet, the resultant field is inclined at
with the
earth's field on (a) its normal bisector and (b) its axis. Magnitude of the
earth's field at the place is given to be 0.42 G. Ignore the length of the
magnet in comparison to the distances involved.
View Answer play_arrow
-
Answer the following questions:
(a) Why does a paramagnetic sample display greater magnetization (for the same magnetizing field) when cooled?
(b) Why is diamagnetism, in contrast, almost independent of temperature?
(c) If a toroid used bismuth for its core, will the field in the core be (slightly) greater of (slightly) less than when the core is empty?
(d) Is the permeability of a ferromagnetic material independent of the magnetic field? If not, is it more for lower of higher field?
(e)Magnetic field lines are always nearly normal to the surface of a ferromagnetic at every point. (This fact is analogous to the static electric field lines being normal to the surface of a conductor at every point). Why?
(f)Would the maximum possible magnetization of a paramagnetic sample be of the same order of magnitude as the magnetization of ferromagnetic?
View Answer play_arrow
-
Answer the following questions:
(a) Explain qualitatively on the basis of domain picture the irreversibility in the magnetisation curve of a ferromagnet.
(b) The hysteresis loop of a soft iron piece has a much smaller area than that of a carbon steel piece. If the material is to go through repeated cycles of magnetization, which piece will dissipate greater heat energy?
(c)‘A system displaying a hysteresis loop such as a ferromagnet is a device for storing memory.' Explain the meaning of this statement.
(d)What kind of ferromagnetic material is used for coating magnetic tapes in a cassette player, or for building ‘memory stores' in a modern computer?
(e)A certain region of space is to be shielded from magnetic fields. Suggest a method.
View Answer play_arrow
-
A long straight horizontal cable carries a current of 2.5 A
in the direction 10° south of west to
north of
east. The magnetic meridian of the place happens to be
west
of the geographic meridian. The earth's magnetic field at the location is 0.33
G, and the angle of dip is zero. Locate the line of neutral points (Ignore the
thickness of the cable). (At neutral points, magnetic field due to a
current-carrying cable is equal and opposite to the horizontal component of
earth's magnetic field.)
View Answer play_arrow
-
A telephone cable at a place has four long straight
horizontal wires carrying a current of 1.0 A in the same direction east to
west. The earth's magnetic field at the place is 0.39 G, and the angle of dip
is
. The magnetic
declination is nearly zero. What are the resultant magnetic fields at points
4.0 cm below the cable?
View Answer play_arrow
-
A compass needle free to turn in a horizon plane is placed
at the centre of circular coil of 30 turns and radius 12 cm. The coil is in a
vertical plane making an angle of
with the
magnetic meridian. When the current in the coil is 0.35 A, the needle points
west to east.
(a) Determine the horizontal component of
the earth?s magnetic field at the location.
(b) The current in the coil is reversed,
and the coil is rotated about its vertical axis by an angle of
in the
anticlockwise sense looking from above. Predict the direction of the needle.
Take the magnetic declination at the place to be zero.
View Answer play_arrow
-
A magnetic dipole is under the
influence of two magnetic fields. The angle between the field directions is
, and one
of the fields has a magnitude of
. If the
dipole comes to stable equilibrium at an angle of
with this
field, what is the magnitude of the other field?
View Answer play_arrow
-
A compass needle free to turn in a horizon plane is placed
at the centre of circular coil of 30 turns and radius 12 cm. The coil is in a
vertical plane making an angle of
with the
magnetic meridian. When the current in the coil is 0.35 A, the needle points
west to east.
(a) Determine the horizontal component of
the earth?s magnetic field at the location.
(b) The current in the coil is reversed,
and the coil is rotated about its vertical axis by an angle of
in the
anticlockwise sense looking from above. Predict the direction of the needle.
Take the magnetic declination at the place to be zero.
View Answer play_arrow
-
A sample of paramagnetic salt contains
atomic
dipoles each of dipole moment
. The
sample is placed under a homogeneous magnetic field of 0.64 T, and cooled to a
temperature of 4.2 K. The degree of magnetic saturation achieved is equal to
15%. What is the total dipole moment of the sample for a magnetic field of 0.98
T and a temperature of 2.8 K? (Assume Curie's law).
View Answer play_arrow
-
A Rowland ring of mean radius 15 cm has 3500 turns of wire
wound on a ferromagnetic core of relative permeability 800.What is the magnetic
field B in the core for a magnetizing current of 1.2 A?
View Answer play_arrow
-
The magnetic moment vectors
and
associated
with the intrinsic spin angular momentum S and orbital angular momentum
,
respectively, of an electron are predicted by quantum theory (and verified
experimental to a high accuracy) to be given by :
,
Which of these relations is in accordance
with the result expected classically? Outline the derivation of the classical
result.
View Answer play_arrow
-
question_answer26)
A toroid of n turns, mean radius R and cross-
sectional radius a carries current . It is placed on a horizontal
table taken as x-y plane.
Its magnetic moment
is non-zero and points in the z-direction by
symmetry
points along the axis of the toroid
is zero, otherwise there would be a field falling as at large distances outside the torioid
is pointing radially outwards
View Answer play_arrow
-
question_answer27)
The magnetic field of Earth can be modeled by that of a
point dipole placed at the centre of the Earth. The dipole axis makes an angle
of with the axis of Earth. At
Mumbai, declination is nearly zero. Then,
the declination varies between W
to
E
the least declination is 0°
the plane defined by dipole axis and Earth
axis passes through Greenwich
declination averaged over Earth must be always-negative
View Answer play_arrow
-
question_answer28)
In a permanent magnet at room temperature
magnetic moment of each molecule is zero
the individual molecules have non-zero magnetic moment
which are all perfectly aligned
domains are partially aligned
domains are all perfectly aligned
View Answer play_arrow
-
question_answer29)
Consider the two idealized systems : (i) a parallel plate
capacitor with large plates and small separation and (ii) a long solenoid of
length L >> R, radius of cross-section. In
(i) is ideally
treated as a constant between plates and zero outside. In (ii) magnetic field is
constant inside the solenoid and zero outside. These idealised assumptions, however,
contradict fundamental laws as below :
case (i) contradicts Gauss's law for electro-
static fields
case (ii) contradicts Gauss's law for magnetic fields.
case (i) agrees with
case (ii) contradicts
View Answer play_arrow
-
question_answer30)
A paramagnetic sample shows a net magneti-
sation of 8 when placed in
an external magnetic field of at a
temperature of 4 K. When the same sample is placed in an external magnetic
field of at a temperature of 16 K, the
magnetisation will be
(a) (b)
(c) (d)
View Answer play_arrow
-
question_answer31)
S is the surface of a lump of magnetic material.
Lines of are necessarily
continuous across S
Some lines of must be
discontinuous across S
Lines of are
necessarily continuous across S
Lines of cannot all be
continuous across S
View Answer play_arrow
-
question_answer32)
The primary origin(s) of magnetism lies in
atomic currents
Pauli exclusion principle
polar nature of molecules
intrinsic spin of electron
View Answer play_arrow
-
question_answer33)
A long solenoid has 1000 turns per metre and
carries a current of 1 A. It has a soft iron core of = 1000. The core is heated beyond
the Curie temperature, .
The field in the
solenoid is (nearly) un-changed but the field
decreases drastically
The and fields in the solenoid are nearly
unchanged
The magnetisation in the core reverses direction
The magnetisation in the core diminishes by a factor of
about
View Answer play_arrow
-
question_answer34)
Essential difference between electrostatic shielding by a
conducting shell and magneto-static shielding is due to
electrostatic field lines can end on charges and conductors
have free charges
lines of can also end
but conductors can not end them
lines of cannot end on
any material and perfect shielding is not possible
shells of high permeability materials can be used to divert
lines of from the interior region
View Answer play_arrow
-
question_answer35)
Let the magnetic field on earth be modeled by that of a
point magnetic dipole at the centre of earth. The angle of dip at a point on
the geographical equator
is always zero
can be zero at specific points
can be positive or negative
is bounded
View Answer play_arrow
-
question_answer36)
A proton has spin and magnetic moment just like an
electron. Why then its effect is neglected in magnetism of materials ?
View Answer play_arrow
-
question_answer37)
A permanent magnet in the shape of a thin cylinder of length
10 cm has M = A/m. Calculate the
magnetisation current . (Here M is the
intensity of magnetisation).
View Answer play_arrow
-
question_answer38)
Explain quantitatively the order of magnitude difference
between the diamagnetic susceptibility of (at
STP) and .
View Answer play_arrow
-
question_answer39)
From molecular view point, discuss the temperature
dependence of susceptibility for diamagnetism, paramagnetism and
ferromagnetism.
View Answer play_arrow
-
question_answer40)
A ball of superconducting material is dipped in liquid
nitrogen and placed near a bar magnet. (i) In which direction will it move?
(ii) What will be the direction of it's magnetic moment?
View Answer play_arrow
-
question_answer41)
Verify the Gauss's law for magnetic field of a point dipole
of dipole moment at the origin for the surface
which is a sphere of radius R.
View Answer play_arrow
-
question_answer42)
Three identical bar magnets are rivetted together at
centre in the same plane as shown in Fig. 3(EP).15. This system is placed at
rest in a slowly varying magnetic field. It is found that the system
of magnets does not show any motion. The north-south poles of one magnet is
shown in the Fig. 3(EP).15. Determine the poles of the remaining two.
View Answer play_arrow
-
question_answer43)
Suppose we want to verify the analogy between electrostatic
and magnetostatic by an explicit experiment. Consider the motion of (i)
electric dipole in an electrostatic
field and (ii) magnetic dipole in a magnetic field . Write down a set of conditions
on so that the two motions are
verified to be identical. (Assume identical initial conditions).
View Answer play_arrow
-
question_answer44)
A bar magnet of magnetic moment M and moment of inertia(about centre, perpendicular to
length) is cut into two equal pieces, perpendicular to length. Let T be the
period of oscillations of the original magnet about an axis through the mid
point, perpendicular to length, in a magnetic field .
What would be the similar period for each piece
?
View Answer play_arrow
-
question_answer45)
Use (i) the Ampere's law for and
(ii) continuity of lines of , to conclude
that inside a bar magnet, (a) lines of run
from the N pole to S pole, while (b) lines of must
run from the S pole to N pole.
View Answer play_arrow
-
question_answer46)
Verify the Ampere's law for magnetic field of a point
dipole of dipole moment . Take C as the
closed curve running clockwise along (i) the z-axis from z = a > 0 to z = R
; (ii) along the quarter circle of radius R and centre at the origin, in the
first quadrant of -z plane ; (iii) along
the -axis from = R to = ,
and (iv) along the quarter circle of radius and
centre at the origin in the first quadrant of -z
plane.
View Answer play_arrow
-
question_answer47)
What are the dimensions of the
magnetic susceptibility? Consider an H-atom. Guess an expression for upto a constant by constructing
a quantity of dimensions of out of
parameters of the atom : Here, is the electronic mass, is electronic velocity, is Bohr radius. Estimate the
number so obtained and compare with the value offor
many solid materials.
View Answer play_arrow
-
question_answer48)
Assume the dipole model for earth's magnetic field B which
is given by = vertical component of magnetic
field; =
Horizontal component of magnetic field ;
= 90° - latitude as measured
from magnetic equator.
Find loci of points for which (i) is minimum; (ii) dip angle is zero;
and (iii) dip angle is ± .
View Answer play_arrow
-
question_answer49)
Consider the plane S formed by the dipole axis and the axis
of earth. Let P be point on the magnetic equator and in S. Let Q be the point
of intersection of the geographical and magnetic equators. Obtain the
declination and dip angles at P and Q.
View Answer play_arrow
-
question_answer50)
There are two current carrying planar coils made each from
identical wires of length L. is circular
(radius R) and is square (side a).
They are so constructed that they have same frequency of oscillation when they
are placed in the same uniform and carry the
same current . Find a in terms of R.
View Answer play_arrow