Next Chapter 2 : Electrostatic Potential And Capacitance >>

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**Exercise : ** Solutions of Questions on Page Number : **46**

Next Chapter 2 : Electrostatic Potential And Capacitance >>
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Q1 :
**
**

What is the force between two small charged spheres having
charges of 2 x
10^{-7} C
and 3 x
10^{-7} C
placed 30 cm apart in air?

**Answer :**

Repulsive force of magnitude 6 ×
10^{ - 3} N

Charge on the first sphere, *q*_{1} = 2
×
10^{ - 7} C

Charge on the second sphere, *q*_{2} = 3
×
10^{ - 7} C

Distance between the spheres, *r* = 30 cm = 0.3 m

Electrostatic force between the spheres is given by the relation,

Where, ∈_{0} =
Permittivity of free space

Hence, force between the two small charged spheres is 6
×
10^{ - 3} N.
The charges are of same nature. Hence, force between them will be
repulsive.

Answer needs Correction? Click Here

Q2 :
**
**

The electrostatic force on a small sphere of charge 0.4 ÃŽÂ¼C due to another small sphere of charge - 0.8 ÃŽÂ¼C in air is 0.2 N. (a) What is the distance between the two spheres? (b) What is the force on the second sphere due to the first?

**Answer :**

**(a)** Electrostatic force on the first sphere, *F* =
0.2 N

Charge on this sphere, *q*_{1} = 0.4
ÃŽÂ¼C = 0.4 ×
10^{ - 6} C

Charge on the second sphere, *q*_{2} =
- 0.8
ÃŽÂ¼C =
- 0.8
×
10^{ - 6} C

Electrostatic force between the spheres is given by the relation,

Where, ∈_{0} =
Permittivity of free space

Answer needs Correction? Click Here

Q3 :
**
**

Check that the ratio *ke*^{2}/*G
m*_{e}*m*_{p}is
dimensionless. Look up a Table of Physical Constants and
determine the value of this ratio. What does the ratio signify?

**Answer :**

Q4 :
**
**

**(a)** Explain the meaning of the statement
'electric charge of a
body is
quantised'.

**(b)** Why can one ignore quantisation of electric charge
when dealing with macroscopic i.e., large scale charges?

**Answer :**

Q5 :
**
**

When a glass rod is rubbed with a silk cloth, charges appear on both. A similar phenomenon is observed with many other pairs of bodies. Explain how this observation is consistent with the law of conservation of charge.

**Answer :**

Q6 :
**
**

Four point charges *q*_{A} = 2
ÃŽÂ¼C, *q*_{B} =
-5
ÃŽÂ¼C, *q*_{C} = 2
ÃŽÂ¼C, and *q*_{D} =
-5
ÃŽÂ¼C are located at the corners of a
square ABCD of side 10 cm. What is the force on a charge of 1
ÃŽÂ¼C placed at the centre of the
square?

**Answer :**

Q7 :
**
**

**(a)** An electrostatic field line is a continuous curve.
That is, a field line cannot have sudden breaks. Why not?

**(b)** Explain why two field lines never cross each other at
any point?

**Answer :**

Q8 :
**
**

Two point charges *q*_{A} = 3
ÃŽÂ¼C and *q*_{B} =
-3
ÃŽÂ¼C are located 20 cm apart in vacuum.

**(a)** What is the electric field at the midpoint O of the
line AB joining the two charges?

**(b)** If a negative test charge of magnitude 1.5
x
10^{-9} C
is placed at this point, what is the force experienced by the
test charge?

**Answer :**

Q9 :
**
**

A system has two charges *q*_{A} = 2.5
x
10^{-7} C
and *q*_{B} =
-2.5
x
10^{-7} C
located at points A: (0, 0,
- 15 cm) and B:
(0, 0, + 15 cm), respectively. What are the total charge and
electric dipole moment of the system?

**Answer :**

Q10 :
**
**

An electric dipole with dipole moment 4
x
10^{-9} C
m is aligned at 30° with the direction
of a uniform electric field of magnitude 5
x 10^{4} N
C^{-1}.
Calculate the magnitude of the torque acting on the dipole.

**Answer :**

Q11 :
**
**

A polythene piece rubbed with wool is found to have a negative
charge of 3 x
10^{-7} C.

**(a)** Estimate the number of electrons transferred (from
which to which?)

**(b)** Is there a transfer of mass from wool to polythene?

**Answer :**

Q12 :
**
**

**(a)** Two insulated charged copper spheres A and B have
their centers separated by a distance of 50 cm. What is the
mutual force of electrostatic repulsion if the charge on each is
6.5 x
10^{-7} C?
The radii of A and B are negligible compared to the distance of
separation.

**(b)** What is the force of repulsion if each sphere is
charged double the above amount, and the distance between them is
halved?

**Answer :**

Q13 :
**
**

Suppose the spheres A and B in Exercise 1.12 have identical sizes. A third sphere of the same size but uncharged is brought in contact with the first, then brought in contact with the second, and finally removed from both. What is the new force of repulsion between A and B?

**Answer :**

Q14 :
**
**

Figure 1.33 shows tracks of three charged particles in a uniform electrostatic field. Give the signs of the three charges. Which particle has the highest charge to mass ratio?

**Answer :**

Q15 :
**
**

Consider a uniform electric field **E** = 3
x 10^{3}
ÃƒÂ®N/C. (a) What is the flux of this field
through a square of 10 cm on a side whose plane is parallel to
the *yz* plane? (b) What is the flux through the same square
if the normal to its plane makes a 60°
angle with the *x*-axis?

**Answer :**

Q16 :
**
**

What is the net flux of the uniform electric field of Exercise 1.15 through a cube of side 20 cm oriented so that its faces are parallel to the coordinate planes?

**Answer :**

Q17 :
**
**

Careful measurement of the electric field at the surface of a
black box indicates that the net outward flux through the surface
of the box is 8.0 x
10^{3} N m^{2}/C. (a) What is the net charge
inside the box? (b) If the net outward flux through the surface
of the box were zero, could you conclude that there were no
charges inside the box? Why or Why not?

**Answer :**

Q18 :
**
**

A point charge +10 ÃŽÂ¼C is a distance 5
cm directly above the centre of a square of side 10 cm, as shown
in Fig. 1.34. What is the magnitude of the electric flux through
the square? (*Hint:* Think of the square as one face of a
cube with edge 10 cm.)

**Answer :**

Q19 :
**
**

A point charge of 2.0 ÃŽÂ¼C is at the centre of a cubic Gaussian surface 9.0 cm on edge. What is the net electric flux through the surface?

**Answer :**

Q20 :
**
**

A point charge causes an electric flux of
-1.0
x 10^{3}
Nm^{2}/C to pass through a spherical Gaussian surface of
10.0 cm radius centered on the charge. (a) If the radius of the
Gaussian surface were doubled, how much flux would pass through
the surface? (b) What is the value of the point charge?

**Answer :**

Q21 :
**
**

A conducting sphere of radius 10 cm has an unknown charge. If the
electric field 20 cm from the centre of the sphere is 1.5
x 10^{3} N/C and points
radially inward, what is the net charge on the sphere?

**Answer :**

Q22 :
**
**

A uniformly charged conducting sphere of 2.4 m diameter has a
surface charge density of 80.0
ÃŽÂ¼C/m^{2}. (a) Find the charge
on the sphere. (b) What is the total electric flux leaving the
surface of the sphere?

**Answer :**

Q23 :
**
**

An infinite line charge produces a field of 9
x 10^{4} N/C at a
distance of 2 cm. Calculate the linear charge density.

**Answer :**

Q24 :
**
**

Two large, thin metal plates are parallel and close to each
other. On their inner faces, the plates have surface charge
densities of opposite signs and of magnitude 17.0
x
10^{-22}
C/m^{2}. What is **E**: (a) in the outer region of the
first plate, (b) in the outer region of the second plate, and (c)
between the plates?

**Answer :**

Q25 :
**
**

An oil drop of 12 excess electrons is held stationary under a
constant electric field of 2.55
x 10^{4} N
C^{-1} in
Millikan's
oil drop experiment. The density of the oil is 1.26 g
cm^{-3}.
Estimate the radius of the drop. (*g* = 9.81 m
s^{-2};
*e* = 1.60 x
10^{-19}
C).

**Answer :**

Q26 :
**
**

Which among the curves shown in Fig. 1.35 cannot possibly represent electrostatic field lines?

**(a)**

**(b)**

**(c)**

**(d)**

**(e)**

**Answer :**

Q27 :
**
**

In a certain region of space, electric field is along the
z-direction throughout. The magnitude of electric field is,
however, not constant but increases uniformly along the positive
*z*-direction, at the rate of 10^{5}
NC^{-1}
per metre. What are the force and torque experienced by a system
having a total dipole moment equal to
10^{-7} Cm
in the negative *z*-direction?

**Answer :**

Q28 :
**
**

(a) A conductor A with a cavity as shown in Fig. 1.36(a) is given
a charge *Q*. Show that the entire charge must appear on the
outer surface of the conductor. (b) Another conductor B with
charge *q* is inserted into the cavity keeping B insulated
from A. Show that the total charge on the outside surface of A is
*Q* + *q* [Fig. 1.36(b)]. (c) A sensitive instrument is
to be shielded from the strong electrostatic fields in its
environment. Suggest a possible way.

**Answer :**

Q29 :
**
**

A hollow charged conductor has a tiny hole cut into its surface. Show that the electric field in the hole is , where is the unit vector in the outward normal direction, and is the surface charge density near the hole.

**Answer :**

Q30 :
**
**

Obtain the formula for the electric field due to a long thin wire
of uniform linear charge density
*ÃŽÂ»* without using
Gauss's law.
[*Hint:* Use
Coulomb's law
directly and evaluate the necessary integral.]

**Answer :**

Q31 :
**
**

It is now believed that protons and neutrons (which constitute
nuclei of ordinary matter) are themselves built out of more
elementary units called quarks. A proton and a neutron consist of
three quarks each. Two types of quarks, the so called
'up'
quark (denoted by u) of charge (+2/3) *e*, and the
'down'
quark (denoted by d) of charge
(-1/3) *e*,
together with electrons build up ordinary matter. (Quarks of
other types have also been found which give rise to different
unusual varieties of matter.) Suggest a possible quark
composition of a proton and neutron.

**Answer :**

Q32 :
**
**

**(a)** Consider an arbitrary electrostatic field
configuration. A small test charge is placed at a null point
(i.e., where **E** = 0) of the configuration. Show that the
equilibrium of the test charge is necessarily unstable.

**(b)** Verify this result for the simple configuration of two
charges of the same magnitude and sign placed a certain distance
apart.

**Answer :**

Q33 :
**
**

A particle of mass *m* and charge
( - *q*) enters
the region between the two charged plates initially moving along
*x*-axis with speed *vx* (like particle 1 in Fig.
1.33). The length of plate is *L* and an uniform electric
field *E* is maintained between the plates. Show that the
vertical deflection of the particle at the far edge of the plate
is *qEL*^{2}/ (2*m*).

*Compare this motion with motion of a projectile in
gravitational field discussed in Section 4.10 of Class XI
Textbook of Physics.*

**Answer :**

Q34 :
**
**

Suppose that the particle in Exercise in 1.33 is an electron
projected with velocity *v*_{x}= 2.0
x 10^{6} m
s^{-1}. If
*E* between the plates separated by 0.5 cm is 9.1
x 10^{2} N/C, where
will the electron strike the upper plate? (| *e* | =1.6
x
10^{-19}
C, *m*_{e} = 9.1
x
10^{-31}
kg.)

**Answer :**

Physics : CBSE ** NCERT ** Exercise Solutions for Class 12th for ** Electric Charges And Fields ** 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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- Chapter 2 - Electrostatic Potential And Capacitance Class 12
- Chapter 3 - Current Electricity Class 12
- Physics Part 2 : Chapter 1 - Ray Optics And Optical Instruments Class 12
- Chapter 4 - Moving Charges And Magnetism Class 12
- Chapter 6 - Electromagnetic Induction Class 12
- Chapter 5 - Magnetism And Matter Class 12
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- Physics Part 2 : Chapter 5 - Nuclei Class 12
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