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A circular coil of wire consisting of 100 turns, each of radius 8.0 cm carries a current of 0.40 A. What is the magnitude of the magnetic field B at the centre of the coil?
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A long straight wire carries a current of 35 A. What is the magnitude of the field B at a point 20 cm from the wire?
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A long straight wire in the horizontal plane carries a current of 50 A in north to south direction. Give the magnitude and direction of B at a point 2.5 m east of the wire.
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A horizontal overhead power line carries a current of 90A in east to west direction. What is the magnitude and direction of the magnetic field due to the current 1.5 in below the line?
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What is the magnitude of magnetic
force per unit length on a wire carrying a current of 8 Aand making an angle of
with the direction of uniform magnetic field of 0.15 T?
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A 
wire carrying a current of 10 A is placed inside a solenoid
perpendicular to its axis. The magnetic field inside the solenoid is given to
be 0.27 T. What is the magnetic force on the wire?
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Two long and parallel straight wires A and B carrying currents of 8.0 A and 5.0 A in the same direction are separated by a distance of 4.0 cm. Estimate the force on a 10 cm section of wire A.
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Two long and parallel straight wires A and B carrying currents of 8.0 A and 5.0 A in the same direction are separated by a distance of 4.0 cm. Estimate the force on a 10 cm section of wire A.
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Two moving coil meters,
and
have
the following particulars:
(The
spring constants are identical for the twometers).
Determine the ratio of (a) current
sensitivityand (b) voltage sensitivity of
and
.
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In a chamber, a uniform magnetic field of
is
maintained. An electron is shot into the field with a speed of
normal
to the field. Explain why the path of the electron is a circle. Determine the
radius of the circular orbit. (
.
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In Exercise 4.11 obtain the frequency of revolution of the electron in its circular orbit. Does the answer depend on the speed of the electron? Explain.
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(a) A circular coil of 30 turns
and radius 8.0 cm carrying a current of 6.0 A is suspended vertically in a
uniform horizontal magnetic field of magnitude 1.0 T. The field lines make an
angle of 
with the normal of the coil. Calculate the magnitude of the
counter torque that must be applied to prevent the coil from turning.
(b) Would your
answer change, if the circular coil in (a) were replaced by a planar coil of
some irregular shape that encloses the same area? (All other particulars are
also unaltered)
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Two concentric circular coils
and
of
radii
and
,
respectively, lie in the same vertical plane containing the north to south
direction. Coil
has 20 turns
and carries a current of 16 A : coil
has 25 turns
and carries a current of 18 A. The sense of the current in
is
anticlockwise, and clockwise in
, for an
observer looking at the coils facing west. Give the magnitude and direction of
the net magnetic field due to the coils at their centre.
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A magnetic field of
is required
which is uniform in a region of linear dimension about
and
area of crosssection about
. The maximum
current carrying capacity of a given coil of wire is 15 A and the number of
turns per unit length that can be wound round a core is at most 1000 turns
.
Suggest some appropriate design particulars of a solenoid for the required
purpose. Assume the core is not ferromagnetic.
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For a circular coil of radius R and N turns carrying I, the
magnitude of the magnetic field at a point on its axis at a distance
from
its centre is given by,
(a) Show that this reduces to the familiar
result for field at the centre of the coil.
(b) Consider two parallel co-axial circular
coils of equal radius R, and number of turns N, carrying equal currents in the
same direction, and separated by a distance R. Show that the field on the axis
around the mid-point between the coils is uniform over a distance that is small
as compared to R, and is given by,
approximately.
(Such an arrangement to produce a nearly
uniform magnetic field over a small region is known as Helmholtz coils.)
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A toroid has a core (non-ferromagnetic) of inner radius 25 cm and outer radius 26 cm, around which 3500 turns of a wire are wound. If the current in the wire is 11 A, what is the magnetic field (i) outside the toroid, (ii) inside the core of the toroid, and (iii) in the empty space surrounded by the toroid.
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Answer the following questions
(a) A magnetic field that varies in magnitude from point to point but has a constant direction (east to west) is set tip in a chamber. A charged particle enters the chamber and travels undeflected along a straight path with constant speed. What can you say about the initial velocity of the particle?
(b) A charged particle enters an environment of a strong and non-uniform magnetic field varying from point to point both in magnitude and direction, and comes out of it following a complicated trajectory. Would its final speed equal the initial speed if it suffered no collisions with the environment?
(c) An electron travelling west to east enters, a chamber having a uniform electrostatic field in north to south direction. Specify the direction in which a uniform magnetic field should be set up to prevent the electron from deflection from its straight line path.
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An electron emitted by a heated
cathode and accelerated through a potential difference of 2.0 kV, enters a
region with uniform magnetic field of 0.15 T. Determine the trajectory of the
electron if the field (a) is transverse to its initial velocity, (b) makes an
angle of 
with the initial velocity.
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A magnetic field set up using Helmholtz coils (described in
Exercise 4.16) is uniform in a small region and has a magnitude of 0.75 T. In
the same region, a uniform electrostatic field is maintained in a direction
normal to the common axis of the coils. A narrow beam of (single species)
charged particle all accelerated through 15 kV enters this region in a
direction perpendicular to both the axis of the coils and the electrostatic
field. If the beam remains undeflected when the electrostatic field is
,
make a simple guess as to what the beam contains. Why is the answer not unique.
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A straight horizontal conducting rod of length 0.45 m and
mass 60 g is suspended by two vertical wires at its ends. A current of 5.0 A is
set up in the rod through the wire.
(a) What magnetic field should be set up
normal to the conductor in order that the tension in the wires is zero?
(b) What will be the total tension in the
Hires if the direction of current is reversed keeping the magnetic field same
as before? (Ignore the mass of the wires.)
.
-
The wires whichconnect the battery of an automobile to its starting motor carry a current of 300 A (for a short time). What is the force per unit length between the wires if they are 70 cm long and 1.5 cm apart? Is the force attractive or repulsive?
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A uniform magnetic field of 1.5 T exists in a cylindrical region of radius 10.0 cm, its direction parallel to the axis along east to west. A wire carrying current of 7.0 A in the north to south direction passes through this region. What is the magnitude and direction of the force on the wire if,
(a) the wire intersects the axis,
(b) the wire is turned from N-S to northeast- northwest direction.
(c) the wire in the N-S direction is lowered from the axis by a distance of 6.0 cm?
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A uniform magnetic field of 3000 G is established along the
positive z-direction. A rectangular loop of sides 10 cm and 5 cm carries a
current of 12 A. What is the torque on the loop in the different cases shown in
Figure? What is the force on each case? Which case corresponds to stable
equilibrium?
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A circular coil of 20 turns and radius 10 cm is placed in a
uniform magnetic field of 0.10 T normal to the plane of the coil. If the
current in the coil is 5.0 A, what is the
(a) total torque on the coil,
(b) total force on the coil,
(c) average force on each electron in the
coil due to the magnetic field ?
(The coil is made of copper wire of
cross-sectional area
and the free
electron density in copper is given to be about
)
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A solenoid 60 cm long and of radius 4.0 cm has 3 layers of
windings of 300 turns each. A 2.0 cm long wire of mass 2.5 g lies inside inside
the solenoid (near its centre) normal to its axis; both the wire and the axis
of the solenoid are in the horizontal plane. The wire is connected through two
leads parallel to the axis of the solenoid to an external battery which
supplies a current of 6.0 A in the wire. What value of current (with
appropriate sense of circulation) in the windings of the solenoid can support
the weight of the wire?
.
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A galvanometer coil has a resistance of
and
the meter shows full scale deflection for a current of 3 mA. How will you
convert the meter into a voltmeter of range 0 to 18 V?
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A galvanometer coil has a resistance of
and
the meter shows full scale deflection for a current of 4 mA. How will you
convert the meter into an ammeter of range 0 to 6 A?
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question_answer28)
Two charged particles
traverse identical helical paths in a completely opposite sense in a uniform
magnetic field 
.
(a) They have equal z-components of momenta
(b) They must have equal charges
(c) They necessarily represent a particle-anti-
particle
pair
(d)
The charge to mass ratio satisfy :
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question_answer29)
Biot-Savart law
indicates that the moving electrons (velocity 
)
produce a magnetic field 
such
that
(a) 
(b)
(c)
it obeys inverse cube law
(d)
it is along the line joining the electron and point of observation
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question_answer30)
A current carrying
circular loop of radius R is placed in the x-y plane with centre at the origin.
Half of the loop with x > 0 is now bent so that it now lies in the y-z
plane.
(a) The magnitude of magnetic moment now diminishes
(b) The
magnetic moment does not change
(c)
The magnitude of at (0,0,z), z
>> R increases
(d)
The magnitude of at (0,0,z), z
>> R is unchanged
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question_answer31)
An electron is
projected with uniform velocity
along the
axis of a current carrying long solenoid. Which of the following is true ?
(a) The electron will be accelerated along the
axis
(b)
The electron path will be circular about the axis
(c)
The electron will experience a force at 45° to the axis and hence execute a
helical path
(d)
The electron will continue to move with uniform velocity along the axis of the solenoid
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question_answer32)
In a cyclotron, a
charged particle
(a) undergoes acceleration all the time.
(b) speeds up between the dees because of the magnetic
field
(c) speeds
up in a dee
(d)
slows down within a dee and speeds up between dees
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question_answer33)
A circular current
loop of magnetic moment M is in an arbitrary orientation in an external
magnetic field . The work done to
rotate the loop by 
about an axis
perpendicular to its plane is
(a)
MB (b) 
(c)
(d)
zero
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question_answer34)
The gyro-magnetic
ratio of an electron in an H-atom, according to Bohr model, is
(a) independent of which orbit it is in
(b)
negative
(c)
positive
(d)
increases with the quantum number n
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question_answer35)
Consider a wire
carrying a steady current, 
placed
in a uniform magnetic field perpendicular
to its length. Consider the charges inside the wire. It is known that magnetic
forces do not work. This implies that
(a) motion
of charges inside the conductor is unaffected by since
they do not absorb energy
(b)
Some charges inside the wire move to the surface as a result of
(c)
if the wire moves under the influence of ,
no work is done by the force
(d)
if the wire moves under the influence of ,
no work is done by the magnetic force on the ions, assumed fixed within the
wire
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question_answer36)
Two identical current
carrying coaxial loops, carry current in
an opposite sense. A simple amperian loop passes through both of them once.
Calling the loop as C,
(a) 
(b) the
value of
is independent of sense of C
(c) there may be a point on C where and 
are perpendicular
(d) vanishes everywhere on C
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question_answer37)
A cubical region of
space is filled with some uniform electric and magnetic fields. An electron
enters the cube across one of its faces with velocity and a positron enters via
opposite face with velocity 
. At this
instant,
(a) the electric forces on both the particles cause identical
accelerations
(b) the magnetic
forces on both the particles cause equal accelerations
(c)
both particles gain or loose energy at the same rate
(d)
the motion of the centre of mass (CM) is determined by alone
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question_answer38)
A charged particle
would continue to move with a constant velocity in a region wherein,
(a) 
= 0, 
(b) 
(c) = 0 (d) = 0, = 0
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question_answer39)
Verify that the cyclotron frequency 
= eB/m has the correct
dimensions of 
.
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question_answer40)
Show that a force that does no work must be a velocity
dependent force.
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question_answer41)
The magnetic force depends on which
depends on the inertial frame of reference. Does then the magnetic force differ
from inertial frame to frame ? Is it reasonable that the net acceleration has a
different value in different frames of reference ?
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question_answer42)
Describe the motion of a charged particle in a cyclotron if
the frequency of the radio frequency (rf) field were doubled.
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question_answer43)
Two long wires carrying current 
and
are arranged as shown in
Fig. 3(EP).1. The one carrying current is
along the x-axis. The other carrying current is
along a line parallel to the y-axis given by x = 0 and z = d.
Find the force exerted at
because
of the wire along the x-axis.
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question_answer44)
A current carrying loop consists of 3 identical quarter
circles of radius R, lying in the positive quadrants of the x-y, y-z and z-x
planes with their centres at the origin, joined together. Find the direction
and magnitude to at the origin.
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question_answer45)
A charged particle of charge e and mass m is moving in an
electric field and magnetic
field . Construct dimensionless
quantities and quantities of dimension .
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question_answer46)
An electron enters with a velocity
into a cubical region
(faces parallel to coordinate planes) in which there are uniform electric and
magnetic fields. The orbit of the electron is found to spiral down inside the
cube in plane parallel to the x-y plane. Suggest a configuration of fields and that can lead to it.
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question_answer47)
Do magnetic forces obey Newton's third law. Verify for two
current elements 
located at the
origin and 
located at (0, R, 0). Both
carry current 
.
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question_answer48)
A multi range voltmeter can be constructed by using a galvanometer
circuit as shown in Fig. 3(EP).3. We want to construct a voltmeter that can
measure 2 V, 20 V and 200 V using a galvanometer of resistance 10 
and that produces maximum
deflection for current of 1 mA. Find 
that
have to be used.
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question_answer49)
A long straight wire carrying current of 25 A rests on a table
as shown in Fig. 3(EP).4. Another wire PQ of length 1 m, mass 2.5 g carries the
same current but in the opposite direction. The wire PQ is free to slide up and
down. To what height will PQ rise?
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question_answer50)
A 100 turn rectangular coil ABCD (in XY plane) is hung from
one arm of a balance (Fig. 3(EP).5). A mass 500 g is added to the other arm to
balance the weight of the coil. A current 
A
passes through the coil and a constant magnetic field of 
T acting inward (in xz plane)
is switched on such that only arm CD of length 1 cm lies in the field. How much
additional mass 'm' must be added to regain the balance?
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question_answer51)
A rectangular conducting loop consists of two wires on two
opposite sides of length joined
together by rods of length d. The wires are each of the same material but with
cross-sections differing by a factor of 2. The thicker wire has a resistance R
and the rods are of low resistance, which in turn are connected to a constant
voltage source 
. The loop is
placed in uniform a magnetic field B at 45 to its plane. Find 
, the torque exerted by the
magnetic field on the loop about an axis through the centres of rods.
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question_answer52)
An electron and a positron are released from (0, 0, 0) and
(0, 0, 
R) respectively, in a
uniform magnetic field = 
, each with an equal
momentum of magnitude p = e BR. Under what conditions on the direction of
momentum will the orbits be non-intersecting circles ?
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question_answer53)
A uniform conducting wire of length 12 a and resistance R
is wound up as a current carrying coil in the shape of (i) an equilateral
triangle of side a; (ii) a square of sides a and, (iii) a regular hexagon of sides
a. The coil is connected to a voltage source .
Find the magnetic moment of the coils in each case.
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question_answer54)
Consider a circular current-carrying loop of radius R in
the x-y plane with centre at origin. Consider the line integral 
(L) =
taken along z-axis.
(a) Show
that (L) monotonically increases
with L.
(b) Use an appropriate Amperian loop to show that
, where is the current in the wire.
(c) Verify directly the above result.
(d) Suppose we replace the circular coil by a square coil
of sides R carrying the same, current .
What can you say about (L) and 
?
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question_answer55)
A multi range current meter can be constructed by using a galvanometer
circuit as shown in Fig. 3(EP).10. We want a current meter that can measure 10
mA, 100 mA and 1 A using a galvanometer of resistance 10 and that produces maximum
deflection for current of 1 mA. Find 
that
have to be used.
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question_answer56)
Five long wires A, B, C, D and E, each carrying current are arranged to form edges
of a pentagonal prism as shown in Fig. 3(EP).11. Each carries current out of
the plane of paper.
(a) What
will be magnetic induction at a point on the axis O? Axis is at a distance R
from each wire.
(b)
What will be the field if current in one of the wires (say A) is switched
off?
(c)
What if current in one of the wire (say) A is reversed ?
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