**Chapter
1, Electric Charges and Fields **

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__NCERT Solutions of 12th CBSE Physics Textbook Exercises__

Question
1.17: Careful measurement of the electric field at the surface of the black box
indicates that the net outward flux through the surface of the box is 8.0 x 10^{3
}Nm^{2}/C

(i)
What is the net charge inside the box?

(ii)
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__:

(ii) We
cannot conclude that the net electric charge inside the box is zero if the
outward flux through the surface of black box is zero because there might be
equal amounts of positive and negative charges cancelling each other and thus
making the resultant charge equal to zero. Thus, we can only conclude that the
net charge inside the box is zero.

Question 1.18: A point charge + 10µC is a distance
5 cm directly above the centre of a square of side 10 cm as shown in figure.
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__: The given square ABCD can be imagined
as one of the side faces of a cube of side 0.10 m. The given charge can be
imagined to be at the centre of this cube at a distance of 5 cm.

Here, q = +
10µC = 10^{-5} C.

Then,
according to the Gauss’s Theorem, the total electric flux through all the 6
faces of the cube is given by -

Question 1.19: A
point charge of 2.0 µC is at the centre of a cubic Gaussian surface 9.0 cm on
edge. What is the net electric flux through the surface?

__Answer__: Here, charge at the centre of the
Gaussian surface,

q = 2µC = 2 x
10^{-6 }C.

ɛ_{o}
= 8.854 x 10^{-12 }C^{2 }N^{-1 }m^{-2}

Ф = electric
flux through it = ?

According to
Gauss’s Theorem, the electric flux through the six faces of the cubes i.e.,
through the Gaussian surface is given by -

Question 1.20: 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 centred 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__: Here, Ф = electric flux through the
spherical Gaussian surface = -1.0 x 10^{3 }Nm^{2 }C^{-1}.

r = radius of
Gaussian spherical surfaces = 10 cm.

Let, q =
charge enclosed at its centre.

(a) According
to Gauss’s law, the electric flux through a Gaussian surface depends upon the
charge enclosed inside the surface and not upon its size. Thus, the electric
flux will remain unchanged i.e., -1.0 x 10^{3 }Nm^{2 }C^{-1}
through the spherical Gaussian surface of double radius i.e. of 20 cm as it
also encloses the same amount of charge.

(b) q = point
charge = ?, ɛ_{o}= 8.854 x 10^{-12 }Nm^{-2}C^{2}.

Question 1.21: 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__: Here, R = radius of the conducting
sphere = 0.10 m

r = distance
of the point from centre of sphere = 20 cm = 0.2 m

Clearly r
> R

E = electric
field at a point at a distance of 20 cm from the sphere = 1.5 x 10^{3}
NC^{-1} acting inward.

q = net
charge on the sphere = ?

Question 1.22: A
uniformly charged conducting sphere of 2.4 m diameter has a surface charge
density of 80.0 µC/m^{2}. (a) Find the charge on the sphere. (b) What
is the total electric flux leaving the surface of the sphere?

__Answer__: Here, σ = surface charge density =
80.0 µC/m^{2}= 80 x 10^{-6 }C/m^{2}

R = radius of the charged sphere = 2.4/2 =
1.2 m.

(a) q = charge on the sphere = ?

Question 1.23: An
infinite line charge produces a field of 9 x 10^{4 }N/C at a distances
of 2 cm. Calculate the linear charge density.

__Answer__: Here, E = electric field produced by
infinite line charge = 9 x 10^{4 }NC^{-1}.

r = distance
of the point where E is produce = 2 cm = 0.02 m.

λ = linear
charge density = ?

Question 1.24: 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, (c) between the plates?

__Answer__:

The
arrangement of the plates is shown in the figure where, σ = surface density of plates = 17.0 x
10^{-22 }Cm^{-2}, ɛ_{o} = 8.854 x 10^{-12} C^{2
}N^{-1}m^{-2}.

(a) E in the
outer region of the first plate = E to the left of the first plate = ? The
region I is to the left of the first plate thus, electric field E_{1 }in
this region due to the two plates is given by the following equation:

(b) E in the
outer region of second plate = E to the right of second plate, i.e., in region
III =?. The E for the region III is given by -

(c) E between
the plates = E in II region = E_{II} =? E_{II} is given by -

** ****Class XII CBSE Physics - Chapter 1, Electric Charges and Fields
- NCERT Solutions**** **

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CBSE Physics Guide - Electric Charges and Fields - Study materials, Additional Objective
Questions, Short Questions & Long Questions, Numerical Problems with
Solutions important for CBSE 12^{th} Board Exam