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Predict the
direction of induced current in the situations described by the following Fig.
2(a) to (f).
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Use Lenz's law to
determine the direction of induced current in the situations describe by
Figure:
(a)
A wire of irregular shape turning into a circular shape
(b)
A circular loop being deformed into narrow straight wire.
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A long solenoid
with 15 turns per cm has a small loop of area placed inside the
solenoid normal to its axis. If the current carried by the solenoid changes
steadily from 2.0 A to 4.0 A in 0.1 s, what is the induced e.m.f. in the loop
while the current is changing?
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A rectangular wire
loop of sides 8 cm and 2 cm with a small cut is moving out of a region of
uniform magnetic field of magnitude 0.3 T directed normal to the loop. What is
the e.m.f. developed across the cut if the velocity of the loop is in a direction
normal to the (a) longer side, (b) shorter side of the loop? For how long does
the induced voltage last in each case?
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A 1.0 m long
metallic rod is rotated with an angular frequency of 400 rad about an axis
normal to the rod passing through its one end. The other end of the rod is in
contact with a circular metallic ring. A constant and uniform magnetic field of
0.5 T parallel to the axis exists everywhere. Calculate the e.m.f. developed
between the centre and the ring.
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A circular coil of
radius 8.0 cm and 20 turns rotates about its vertical diameter with an angular
speed of 500 rad in a uniform
horizontal magnetic field of magnitude . Obtain the
maximum and average emf induced in the coil. If the coil forms a closed loop of
resistance 10 , calculate the
maximum value of current in the coil. Calculate the average power loss due to
Joule beating. Where does this power come from?
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A horizontal
straight wire 10 m long extending from east to west is falling with a speed of , at right angles
to the horizontal component of the earth's magnetic field, .
(a)
What is the instantaneous value of the e.m.f. induced in the wire?
(b)
What is the direction of the e.m.f.?
(c)
Which end of the wire is at the higher electrical potential?
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Current in a circuit falls from 5.0 A to 0.0 A s. If an average end of 200 V induced, give an estimate of the self-inductance of the circuit.
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A pair of adjacent coils has a mutual inductance of 1.5 H. If the current in one coil changes from 0 to 20 A in 0.5 s, what is the change of flux linkage with the other coil?
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A jet plane is
travelling towards west at a speed of 1800 km/h. What is the voltage difference
developed between the ends of the wing having a span of 25 m, if the Earth
magnetic field at the location has a magnitude of and the dip angle
is ?
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Suppose the loop in
Exercise 6.4 is stationer, but the current feeding the electromagnet that
produces the magnetic field is gradually reduced so that the field decreases
from its initial value of 0.3 T at the rate of 0.02 T . If the cut is
joined and the loop has a resistance of 1.6, how much power
dissipated by the loop as heat? What is the source of this power?
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A square loop of
side 12 cm with its side parallel to and axes is moved with
velocity of in the positive
direction in an environment containing magnetic field in the positive
z-direction. The field is neither uniform in space nor constant in time. It has
a gradient of along the negative
x-direction (that is increases by as one moves the
negative x-direction), and it is decreasing in time at the rate of . Determine the
direction and magnitude of the induced current the loop if its resistance is .
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It is desired to
measure the magnitude of field between the poles of a powerful loud speaker
magnet. A small flat search coil of area with 25 closely
would turns, is positioned normal to the field direction, and then quickly
snatched out of the field region. Equivalently, one can give it a quick turn to bring its
plane parallel to the field direction. The total charge flown in the coil
(measured by a ballistic galvanometer connected to coil) is 7.5 mC. The
combined resistance of he coil and the galvanometer is . Estimate the
field strength of magnet.
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Figure shows a
metal rod PQ resting on the rails AB and positioned between the poles of a
permanent magnet. The rails, the rod, and the magnetic field are in three
mutual perpendicular directions. A galvanometer G connects the rails through a
switch K.
Length
of the rod = 15 cm, B = 0.50 T,resistance of the closed loop containing the rod
= 9.0 m . Assume the
field to be uniform.
(a)
Suppose K is open and the rod is moved with a speed of 12 cm in the direction
shown. Give the polarity and magnitude of the induced emf.
(b)
Is there an excess charge built up at the ends of the rods when K is open? What
if K is closed?
(c)
With K open and the rod moving uniformly, there is no net force on the
electrons in the rod PQ even though they do experience magnetic force due to
the motion of the rod. Explain.
(d)
What is the retarding force on the rod when K is closed?
(e)
How much power is required (by an external agent) to keep the rod moving at the
same speed when K is closed?
How much power is required when K is open?
(f)
How much power is dissipated as heat in the closed circuit? What is the source
of this power?
(g)
What is the induced emf in the moving rod if the magnetic field is parallel to
the rails instead of being perpendicular?
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An air-cored
solenoid with length 30 cm, area of cross-section and number of turns
500, carries a current of 2.5 A. The current is suddenly switched off in a
brief time of . How much is the
average back emf induced across the ends of the open switch in the circuit?
Ignore the variation in magnetic field near the ends of the solenoid.
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(a) Obtain an
expression for the mutual inductance between a long straight wire and a square
loop of side a as shown in Figure.
(b)
Now assume that the straight wire carries a current of 50 A and the loop is
moved the right with a constant velocity, = 10 m/s.
Calculate the induced e.m.f. in loop at the instant when = 0.2
m. Take = 0.1 m and assume that the loop has j large resistance.
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The line charge per
unit length is lodged uniformly onto the rim of a wheel of mass M and radius R.
The wheel has light non-conducting spokes and is free to rotate without
friction about its axis (Figure). A uniform magnetic field extends over a
circular magnetic field extends over a circular region within the rim. It given
by
= 0 [otherwise]
What
is the angular velocity of the wheel after the field is suddenly switched off?
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question_answer18)
A square of side L
meters lies in the x-y plane in a region, where the magnetic field is given by , where is constant. The magnitude
of flux passing through the square is
(a) (b)
(c)
(d)
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question_answer19)
A loop, made of
straight edges has six corners
at A (0, 0,
0), B (L, O, 0), C (L, L, 0), D (0, L, 0), E (0, L, L) and F (0, 0, L). A magnetic
field is present in the region.
The flux passing through the loop ABCDEFA (in that order) is
(a)
(b)
(c)
(d)
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question_answer20)
A cylindrical bar
magnet is rotated about its axis. Fig. 4(EP).1. A wire is connected from the
axis and is made to touch the cylindrical surface through a contact. Then
(a) a
direct current flows in the ammeter A
(b) no current flows through the ammeter A
(c) an alternating sinusoidal current flows through the
ammeter A with a time period
(d) a time
varying non-sinosoidal current flows through the ammeter A
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question_answer21)
There are two coils A
and B as shown in Fig. 4(EP).2. A current starts flowing in B as shown, when A
is moved towards B and stops when A stops moving. The current in A is counter-
clockwise. B is kept stationary when A moves. We can infer that
(a)
there is a constant current in the clockwise
direction
in A
(b)
there is a varying current in A
(c) there
is no current in A
(d) there is a constant current in the counter-
clockwise
direction in A
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question_answer22)
Same as problem 4
except the coil A is made to rotate about a vertical axis, Fig. 4(EP).3. No
current flows in B it A is at rest. The current in coil A, when the current in
B (at t = 0) is counterclockwise and the coil A is as shown at this istant, t =
0, is
(a) constant
current clockwise
(b) varying current clockwise
(c) varying current counterclockwise
(d) constant current counterclockwise
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question_answer23)
The self inductance L
of a solenoid of length
and area of
cross-section A, with a fixed number of turns N increases as
(a) and A increase
(b) decreases and A
increases
(c) increases and A
decreases
(d) both and A
decrease
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question_answer24)
A metal plate is
getting heated. It can be because
(a) a direct current is passing through the plate
(b) it is placed in a time varying magnetic field
(c) it is placed in a space varying magnetic field, but
does not vary with time
(d) a current (either direct or alternating) is passing
through the plate
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question_answer25)
An e.m.f. is produced
in a coil, which is not connected to an external voltage source. This can be
due to
(a) the coil being in a time varying magnetic field
(b) the coil moving in a time varying magnetic
field
(c) the
coil moving in a constant magnetic field
(d) the coil is stationary in external spatially varying
magnetic field, which does not change with time
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question_answer26)
The mutual inductance of coil 1 with respect to
coil 2
(a) increases when they are brought nearer
(b) depends on the current passing through the coils
(c)
increases when one of them is rotated about an axis
(d) is the same as of
coil 2 with respect to
coil 1
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question_answer27)
A circular coil
expands radially in a region of magnetic field and no electromotive force is produced
in the coil. This can be because
(a) the magnetic field is constant
(b) the magnetic field is in the same plane as the circular
coil and it may or may not vary
(c) the
magnetic field has a perpendicular (to the plane of the coil) component whose magnitude
is decreasing suitably
(d) there is a constant magnetic field in the perpendicular
(to the plane of the coil) direction
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question_answer28)
Consider a magnet surrounded by a wire with an on/off
switch S, Fig. 4(EP).5. If the switch is thrown from the off position (open
circuit) to the on position (closed circuit), will a current flow in the
circuit? Explain.
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question_answer29)
A wire in the form of a tightly wound solenoid is connected
to a DC source, and carries a current. If the coil is stretched so that there
are gaps between successive elements of the spiral coil, will the current
increase or decrease? Explain.
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question_answer30)
A solenoid is connected to a battery so that a steady
current flows through it. If an iron core is inserted into the solenoid, will the
current increase or decrease? Explain.
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question_answer31)
Consider a metal ring kept on top of a fixed solenoid (say
on a cardboard), Fig. 4(EP).6. The centre of the ring coincides with the axis
of the solenoid. If the current is suddenly switched on, the metal ring jumps
up. Explain.
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question_answer32)
Consider a metal ring kept (supported by a cardboard) on
top of a fixed solenoid carrying a current ,
Fig. 4(EP).6. The centre of the ring coincides with the axis of the solenoid.
If the current in the solenoid is switched off, what will happen to the ring?
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question_answer33)
Consider a metallic pipe with an inner radius of 1 cm. If a
cylindrical bar magnet of radiuscm is dropped
through the pipe, it takes more time to come down than it takes for a similar
unmagnetised cylindrical iron bar dropped through the metallic pipe. Explain.
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question_answer34)
A magnetic field in a certain region is given by and a coil of radius with resistance R is placed
in the x-y plane with its centre at the origin in the magnetic field, Fig.
4(EP).7. Find the magnitude and the direction of the current at (, 0, 0) at and
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question_answer35)
Consider a closed loop C in a magnetic field, Fig. 4(EP).8.
The flux passing through the loop is defined by choosing a surface whose edge
coincides with the loop and using the formula ..... Now if we chose two
different surfacesand having C as their edge,
would we get the same answer for flux. Justify your answer.
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question_answer36)
Find the current in the wire PQ for the configuration shown
in Fig. 4(EP).9. Wire PQ has negligible resistance. B, the magnetic field is
coming out of the paper. is a
fixed angle made by PQ travelling smoothly over two conducting parallel wires separated
by a distance d.
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question_answer37)
A (current vs time) graph of the current passing through a
solenoid is shown in Fig. 4(EP).10. For which time is the back electromotive
force a maximum? If the back emf
at t = 3 s is e, find the back emf at t = 7 s, 15 s and 40 s. OA, AB and BC are
straight line segments.
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question_answer38)
There are two coils A and B separated by some distance. If
a current of 2 A flows through A, a magnetic flux of Wb passes through B (no
current through B). If no current passes through A and a current of 1 A passes
through B, what is the flux through A?
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question_answer39)
A magnetic field covers
a large region where a wire AB slides smoothly over two parallel conductors
separated by a distance d, Fig. 4(EP).11. The wires are in the x-y plane. The
wire AB (of length d) has resistance R and the parallel wires have negligible
resistance. If AB is moving with velocity ,
what is the current in the circuit? What is the force needed to keep the wire moving
at constant velocity?
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question_answer40)
A conducting wire XY of mass m and negligible resistance
slides smoothly on two parallel conducting wires as shown in Fig. 4(EP).12. The
closed circuit has a resistance R due to AC. AB and CD are perfect conductors.
There is a magnetic field B =. (i)
Write down equation for the acceleration of the wire XY. (ii) If B is
independent of time, obtain (t),
assuming (0) = . (iii) For (b), show that the
decrease in kinetic energy of XY equals the heat lost in R.
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question_answer41)
ODBAC is a fixed rectangular conductor of negligible
resistance (CO is not connected) and OP is a conductor which rotates clockwise
with an angular velocity , Fig.
4(EP).13. The entire system is in a uniform magnetic field B whose direction is
along the normal to the surface of the rectangular conductor ABDC. The
conductor OP is in electric contact with ABDC. The rotating conductor has a
resistance of per unit length.
Find the current in the rotating conductor, as it rotates by 180.
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question_answer42)
Consider an infinitely long wire carrying a current (t), with = constant. Find the
current produced in the rectangular loop of wire ABCD if its resistance is R, Fig.
4(EP).17.
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question_answer43)
A rectangular loop of wire ABCD is kept close to an infinitely
long wire carrying a current
for and for t > T, Fig. 4(EP).18.
Find the total charge passing through a given point in the loop, in time . The resistance of the
loop is R.
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question_answer44)
A magnetic field B is confined to a region r a and points out of the
paper (the z-axis), r = 0 being the centre of the circular region. A charged
ring (charge = Q) of radius b, b > a and mass m lies in the x-y plane with
its centre at the origin. The ring is free to rotate and is at rest. The
magnetic field is brought to zero in time .
Find the angular velocity of the
ring after the field vanishes.
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question_answer45)
A rod of mass m and resistance R slides smoothly over two parallel
perfectly conducting wires kept sloping at an angle with
respect to the horizontal, Fig. 4(EP).19. The circuit is closed through a
perfect conductor at the top. There is a constant magnetic field B along the
vertical direction. If the rod is initially at rest, find the velocity of the
rod as a function of time.
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question_answer46)
Find the current in the sliding rod AB (resistance = R) for
the arrangement shown in Fig. 4(EP).20. B is constant and is out of the paper.
Parallel wires have no resistance. is
constant. Switch S is closed at time t = 0.
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question_answer47)
Find the current in the sliding rod AB (resistance = R) for
the arrangement shown in Fig. 4(EP).21. B is constant and is out of the paper.
Parallel wires have no resistance, is constant.
Switch S is closed at time t = 0.
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question_answer48)
A metallic ring of mass m and radius (ring being horizontal) is
falling under gravity in a region having a magnetic field. If z is the vertical
direction, the z-component of magnetic field is .
If R is the resistance of the ring and if the ring falls with a velocity , find the energy lost in
the resistance. If the ring has reached a constant velocity, use the
conservation of energy to determine in terms
of m, B, and acceleration due to
gravity g.
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question_answer49)
A long solenoid 'S' has ?n? turns per meter, with diameter
''. At the centre of this
coil, we place a smaller coil of 'N ' turns and diameter 'b' (where b < a).
If the current in the solenoid increases linearly with time, what is the induced
emf appearing in the smaller coil. Plot graph showing nature of variation in
emf, if current varies as a function of
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