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**Exercise : ** Solutions of Questions on Page Number : **229**

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Q1 :
**
**

Predict the direction of induced current in the situations described by the following Figs. 6.18(a) to (f ).

**(a)**

**(b)**

**(c)**

**(d)**

**(e)**

**(f)**

**Answer :**

The direction of the induced current in a closed loop is given by Lenz's law. The given pairs of figures show the direction of the induced current when the North pole of a bar magnet is moved towards and away from a closed loop respectively.

Using Lenz's rule, the direction of the induced current in the given situations can be predicted as follows:

**(a)** The direction of the induced current is along
**qrpq***.*

**(b)** The direction of the induced current is along
**prqp**.

**(c)** The direction of the induced current is along
* yzxy*.

**(d)** The direction of the induced current is along
* zyxz*.

**(e)** The direction of the induced current is along
* xryx*.

**(f)** No current is induced since the field lines are lying
in the plane of the closed loop.

Answer needs Correction? Click Here

Q2 :
**
**

Use Lenz's law to determine the direction of induced current in the situations described by Fig. 6.19:

**(a)** A wire of irregular shape turning into a
circular shape;

**(b)** A circular loop being deformed into a narrow
straight wire.

**Answer :**

According to
Lenz's law, the
direction of the induced *emf* is such that it tends to
produce a current that opposes the change in the magnetic flux
that produced it.

**(a)** When the shape of the wire changes, the flux
piercing through the unit surface area increases. As a result,
the induced current produces an opposing flux. Hence, the induced
current flows along adcb.

**(b)** When the shape of a circular loop is deformed
into a narrow straight wire, the flux piercing the surface
decreases. Hence, the induced current flows along

Answer needs Correction? Click Here

Q3 :
**
**

A long solenoid with 15 turns per cm has a small loop of area 2.0
cm^{2} 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 emf in the loop while the
current is changing?

**Answer :**

Q4 :
**
**

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 emf developed
across the cut if the velocity of the loop is 1 cm
s^{-1} 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?

**Answer :**

Q5 :
**
**

A 1.0 m long metallic rod is rotated with an angular
frequency of 400 rad
s^{-1}
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 emf developed between the
centre and the ring.

**Answer :**

Q6 :
**
**

A circular coil of radius 8.0 cm and 20 turns is rotated about
its vertical diameter with an angular speed of 50 rad
s^{-1} in
a uniform horizontal magnetic field of magnitude
3.0 x 10^{-2}
T. Obtain the maximum and average emf induced in the coil. If the
coil forms a closed loop of resistance
10ÃŽÂ©, calculate the maximum value of
current in the coil. Calculate the average power loss due to
Joule heating. Where does this power come from?

**Answer :**

Q7 :
**
**

A horizontal straight wire 10 m long extending from east to west
is falling with a speed of 5.0 m
s^{-1}, at
right angles to the horizontal component of the
earth's
magnetic field, 0.30 x
10^{-4} Wb
m^{-2}.

**(a)** What is the instantaneous value of the emf induced in
the wire?

**(b)** What is the direction of the emf?

**(c)** Which end of the wire is at the higher electrical
potential?

**Answer :**

Q8 :
**
**

Current in a circuit falls from 5.0 A to 0.0 A in 0.1 s. If an average emf of 200 V induced, give an estimate of the self-inductance of the circuit.

**Answer :**

Q9 :
**
**

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?

**Answer :**

Q10 :
**
**

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's
magnetic field at the location has a magnitude of 5
x
10^{-4} T
and the dip angle is 30°.

**Answer :**

Q11 :
**
**

Suppose the loop in Exercise 6.4 is stationary 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
s^{-1}. If
the cut is joined and the loop has a resistance of 1.6
ÃŽÂ© how much power is dissipated by the
loop as heat? What is the source of this power?

**Answer :**

Q12 :
**
**

A square loop of side 12 cm with its sides parallel to X and Y
axes is moved with a velocity of 8 cm
s^{-1} in
the positive *x-*direction in an environment containing a
magnetic field in the positive *z*-direction. The field is
neither uniform in space nor constant in time. It has a gradient
of 10^{-3}
T cm^{-1}
along the negative *x-*direction (that is it increases by
10^{- 3} T
cm^{-1} as
one moves in the negative *x*-direction), and it is
decreasing in time at the rate of
10^{-3} T
s^{-1}.
Determine the direction and magnitude of the induced current in
the loop if its resistance is 4.50 mÃŽÂ©.

**Answer :**

Q13 :
**
**

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 2 cm^{2} with 25 closely wound turns, is positioned
normal to the field direction, and then quickly snatched out of
the field region. Equivalently, one can give it a quick
90° 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 the coil and the galvanometer is
0.50 ÃŽÂ©. Estimate the field strength of
magnet.

**Answer :**

Q14 :
**
**

Figure 6.20 shows a metal rod PQ resting on the smooth 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
mÃŽÂ©. Assume the field to be uniform.

**(a)** Suppose K is open and the rod is moved with a speed of
12 cm
s^{-1} 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 (=12 cm
s^{-1})
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?

**Answer :**

Q15 :
**
**

An air-cored solenoid with length 30 cm, area of cross-section 25
cm^{2} and number of turns 500, carries a current of 2.5
A. The current is suddenly switched off in a brief time of
10^{-3} s.
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.

**Answer :**

Q16 :
**
**

**(a)** Obtain an expression for the mutual inductance between
a long straight wire and a square loop of side *a* as shown
in Fig. 6.21.

**(b)** Now assume that the straight wire carries a current of
50 A and the loop is moved to the right with a constant velocity,
*v* = 10 m/s.

Calculate the induced emf in the loop at the instant when
*x* = 0.2 m.

Take *a* = 0.1 m and assume that the loop has a large
resistance.

**Answer :**

Q17 :
**
**

A line charge ÃŽÂ» 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 (Fig. 6.22). A
uniform magnetic field extends over a circular region within the
rim. It is given by,

**B** = -
B_{0} **k** (*r*
Ã¢”°Â¤ *a*;
*a* < *R*)

= 0 (otherwise)

What is the angular velocity of the wheel after the field is suddenly switched off?

**Answer :**

Physics : CBSE ** NCERT ** Exercise Solutions for Class 12th for ** Electromagnetic Induction ** will be available online in PDF book form soon. The solutions are absolutely Free. Soon you will be able to download the solutions.

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