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**Exercise : ** Solutions of Questions on Page Number : **169**

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Q1 :
**
**

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?

**Answer :**

Number of turns on the circular coil, *n* = 100

Radius of each turn,*r* = 8.0 cm = 0.08 m

Current flowing in the coil, *I* = 0.4 A

Magnitude of the magnetic field at the centre of the coil is given by the relation,

Where,

= Permeability of free space

= 4π ×
10^{â€“7} T m
A^{â€“1}

Hence, the magnitude of the magnetic field is 3.14
×
10^{â€“4} T.

Answer needs Correction? Click Here

Q2 :
**
**

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?

**Answer :**

Current in the wire, *I* = 35 A

Distance of a point from the wire, *r* = 20 cm = 0.2 m

Magnitude of the magnetic field at this point is given as:

*B*

Where,

=
Permeability of free space = 4π
×
10^{â€“7} T m
A^{â€“1}

Hence, the magnitude of the magnetic field at a point 20 cm from
the wire is 3.5 ×
10^{â€“5} T.

Answer needs Correction? Click Here

Q3 :
**
**

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.

**Answer :**

Q4 :
**
**

A horizontal overhead power line carries a current of 90 A in east to west direction. What is the magnitude and direction of the magnetic field due to the current 1.5 m below the line?

**Answer :**

Q5 :
**
**

What is the magnitude of magnetic force per unit length on a wire carrying a current of 8 A and making an angle of 30º with the direction of a uniform magnetic field of 0.15 T?

**Answer :**

Q6 :
**
**

A 3.0 cm 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?

**Answer :**

Q7 :
**
**

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.

**Answer :**

Q8 :
**
**

A closely wound solenoid 80 cm long has 5 layers of windings of
400 turns each. The diameter of the solenoid is 1.8 cm. If the
current carried is 8.0 A, estimate the magnitude of **B**
inside the solenoid near its centre.

**Answer :**

Q9 :
**
**

A square coil of side 10 cm consists of 20 turns and carries a current of 12 A. The coil is suspended vertically and the normal to the plane of the coil makes an angle of 30º with the direction of a uniform horizontal magnetic field of magnitude 0.80 T. What is the magnitude of torque experienced by the coil?

**Answer :**

Q10 :
**
**

Two moving coil meters, M_{1} and M_{2} have the
following particulars:

*R*_{1} = 10 ÃŽÂ©,
*N*_{1} = 30,

*A*_{1} = 3.6 x
10^{-3} m^{2}*,*
*B*_{1} = 0.25 T

*R*_{2} = 14 ÃŽÂ©,
*N*_{2} = 42,

*A*_{2} = 1.8 x
10^{-3} m^{2},
*B*_{2} = 0.50 T

(The spring constants are identical for the two meters).

Determine the ratio of (a) current sensitivity and (b) voltage
sensitivity of M_{2} and M_{1}.

**Answer :**

Q11 :
**
**

In a chamber, a uniform magnetic field of 6.5 G (1 G =
10^{-4} T) is maintained. An electron
is shot into the field with a speed of 4.8
x 10^{6} m
s^{-1} normal to the field. Explain
why the path of the electron is a circle. Determine the radius of
the circular orbit. (*e* = 1.6
x
10^{-19} C,
*m*_{e}=
9.1 x 10^{-31}
kg)

**Answer :**

Q12 :
**
**

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.

**Answer :**

Q13 :
**
**

**(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 60º 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.)

**Answer :**

Q14 :
**
**

Two concentric circular coils X and Y of radii 16 cm and 10 cm, respectively, lie in the same vertical plane containing the north to south direction. Coil X has 20 turns and carries a current of 16 A; coil Y has 25 turns and carries a current of 18 A. The sense of the current in X is anticlockwise, and clockwise in Y, 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.

**Answer :**

Q15 :
**
**

A magnetic field of 100 G (1 G =
10^{-4} T)
is required which is uniform in a region of linear dimension
about 10 cm and area of cross-section about
10^{-3}
m^{2}. 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
m^{-1}.
Suggest some appropriate design particulars of a solenoid for the
required purpose. Assume the core is not ferromagnetic

**Answer :**

Q16 :
**
**

For a circular coil of radius *R* and *N* turns
carrying current *I*, the magnitude of the magnetic field at
a point on its axis at a distance *x* 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*.]

**Answer :**

Q17 :
**
**

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 (a) outside the toroid, (b) inside the core of the toroid, and (c) in the empty space surrounded by the toroid.

**Answer :**

Q18 :
**
**

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 up 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 deflecting from its straight
line path.

**Answer :**

Q19 :
**
**

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 30º with the initial velocity.

**Answer :**

Q20 :
**
**

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 particles 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 9.0 x
10^{-5} V
m^{-1},
make a simple guess as to what the beam contains. Why is the
answer not unique?

**Answer :**

Q21 :
**
**

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 wires.

**(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 wires if the
direction of current is reversed keeping the magnetic field same
as before? (Ignore the mass of the wires.) g = 9.8 m
s^{-2}.

**Answer :**

Q22 :
**
**

The wires which connect 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?

**Answer :**

Q23 :
**
**

A uniform magnetic field of 1.5 T exists in a cylindrical region of radius10.0 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?

**Answer :**

Q24 :
**
**

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 Fig. 4.28? What is the force
on each case? Which case corresponds to stable equilibrium?

**Answer :**

Q25 :
**
**

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
10^{-5}
m^{2}, and the free electron density in copper is given
to be about 10^{29}
m^{-3}.)

**Answer :**

Q26 :
**
**

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 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? *g* = 9.8 m
s^{-2}

**Answer :**

Q27 :
**
**

A galvanometer coil has a resistance of 12 ÃŽÂ© and the metre shows full scale deflection for a current of 3 mA. How will you convert the metre into a voltmeter of range 0 to 18 V?

**Answer :**

Q28 :
**
**

A galvanometer coil has a resistance of 15 ÃŽÂ© and the metre shows full scale deflection for a current of 4 mA. How will you convert the metre into an ammeter of range 0 to 6 A?

**Answer :**

Physics : CBSE ** NCERT ** Exercise Solutions for Class 12th for ** Moving Charges And Magnetism ** 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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