Print

Future Chef Institute

PRACTICE WORK
Class 12 - Physics
Time Allowed: 3 hours Maximum Marks: 94
1. If 109 electrons move out of a body to another body every [2]
second, how much time is required to get a total charge of 1 C
on the other body?
2. How can you charge a metal sphere positively without touching [3]
it?
3. How much positive and negative charge is there in a cup of [2]
water?
4. Coulomb’s law for the electrostatic force between two point [5]
charges and Newton’s law for gravitational force between two
stationary point masses, both have inverse-square dependence
on the distance between the charges and masses respectively.
a. Compare the strength of these forces by determining the ratio
of their magnitudes
i. for an electron and a proton and
ii. for two protons.
b. Estimate the accelerations of electron and proton due to the
o

electrical force of their mutual attraction when they are 1A (=

10-10 m) apart? (mp = 1.67 × 10-27 kg, me = 9.11 × 10-31
kg).
5. A charged metallic sphere A is suspended by a nylon thread. [3]
Another charged metallic sphere B held by an insulating handle
is brought close to A such that the distance between their
centres is 10 cm, as shown in Fig (a). The resulting repulsion of
A is noted (for example, by shining a beam of light and
measuring the deflection of its shadow on a screen). Spheres A
and B are touched by uncharged spheres C and D respectively,
as shown in Fig (b). C and D are then removed and B is brought
 closer to A distance of 5.0 cm between their centres, as shown
in Fig (c). What is the expected repulsion of A on the basis of
Coulomb’s law? Spheres A and C and spheres B and D have
identical sizes. Ignore the sizes of A and B in comparison to the
separation between their centres.

6. Consider three charges q1, q2, q3 each equal to q at the vertices [3]
of an equilateral triangle of side l. What is the force on a charge
Q (with the same sign as q) placed at the centroid of the
triangle, as shown in a fig?

7. Consider the charges q, q, and –q placed at the vertices of an [3]

equilateral triangle, as shown in fig. What is the force on each
charge?

8. An electron falls through a distance of 1.5 cm in a uniform [2]

electric field of magnitude 2.0 × 104 N C-1 [Fig (a)]. The
direction of the field is reversed keeping its magnitude
 unchanged and a proton falls through the same distance [Fig
(b)]. Compute the time of fall in each case. Contrast the
situation with that of free fall under gravity.

9. Two-point charges q1 and q2, of magnitude +10-8 C and -10-8 C, [3]

respectively, are placed 0.1 m apart. Calculate the electric fields
at points A, B, and C shown in fig.

10. Two charges ± 10 μC are placed 5.0 mm apart. Determine the [2]
electric field at
a. a point on the axis of the dipole 15 cm away from its centre O
on the side of the positive charge, as shown in figure.

b. a point Q, 15 cm away from O on a line passing through O and

normal to the axis of the dipolem, as shown in figure.

11. The electric field components in fig. are Ex = αx1/2, Ey = Ez = 0, [3]

in which α = 800 N/C m1/2. Calculate

 a. the flux through the cube, and
b. the charge within the cube. Assume that a = 0.1 m.
12. An electric field is a uniform, and in the positive x-direction for [5]
positive x, and uniform with the same magnitude but in the
negative x-direction for negative x. It is given that E⃗ = 200 ^i N/C
for x > 0 and E⃗ = –200 ^i N/C for x < 0. A right circular cylinder of
length 20 cm and radius 5 cm has its centre at the origin and its
axis along the x-axis so that one face is at x = +10 cm and the
other is at x = -10 cm (Fig).

a. What is the net outward flux through each flat face?

b. What is the flux through the side of the cylinder?
c. What is the net outward flux through the cylinder?
d. What is the net charge inside the cylinder?
13. An early model for an atom considered it to have a positively [5]
charged point nucleus of charge Ze, surrounded by a uniform
density of negative charge up to a radius R. The atom as a whole
is neutral. For this model, what is the electric field at a distance r
from the nucleus?

14. What is the force between two small charged spheres having [1]
charges of 2 × 10-7C and 3 × 10-7C placed 30 cm apart in air?
15. The electrostatic force on a small sphere of charge 0.4 μC due [2]
to another small sphere of charge -0.8 μC 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?

16. Check that the ratio ke

2

is dimensionless. Look up a table of [3]

Gme mp

physical constants and determine the value of this ratio. What

does this ratio signify?

17. a. Explain the meaning of the statement, electric charge of a [2]

body is quantized.
b. Why can one ignore quantization of electric charge when
dealing with macroscopic i.e. large scale charges?
18. When a glass rod is rubbed with a silk cloth, charges appear on [3]
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.
19. Four point charges qA = 2μC, qB = -5μC, qC = 2μC and qD = -5μC [2]
are located at the corners of a square ABCD of side 10 cm. What
is the force on a charge of 1μC placed at the centre of the
square?

20. a. An electrostatic field line is a continuous curve. That is, a field [2]
cannot have sudden breaks. Why not?
b. Explain why two field lines never cross each other at any
point?
21. Two-point charges qA = +3μC and qB = -3μC are located 20 cm [3]
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× 10-9 C is placed at
this point, what is the force experienced by the test charge?

22. A system has two charges qA = 2.5 × 10-7C and qB = -2.5 × 10- [2]
7C located at points A: (0, 0, -15 cm) and B : (0, 0, +15 cm),
respectively. What is the total charge and electric dipole
moment of the system?
23. An electric dipole with dipole moment 4 × 10-9 Cm is aligned at [1]
30o with the direction of a uniform electric field of magnitude 5
× 104 NC-1. Calculate the magnitude of the torque acting on the
dipole.
24. A polythene piece rubbed with wool is found to have a negative [3]
charge of 3 × 10-7C.
a. Estimate the number of electrons transferred (from which to
which)?
b. Is there a transfer of mass from wool to polythene?

25. a. Two insulated charged copper spheres A and B have their [3]
centres separated by a distance of 50 cm. What is the mutual
force of electrostatic repulsion if the charge on each is
C ? The radii of A and B are negligible compared to
−7
6.5 × 10

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?
26. Figure shows tracks of three charged particles in a uniform [2]
electrostatic field. Give the signs of the three charges. Which
particle has the highest charge to mass ratio?

27. Consider a uniform electric field E 3

= 3 × 10 ^i N /C . [3]

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?

28. What is the net flux of the uniform electric field of E⃗ = 3 × 103 ^i [2]
N/C through a cube of side 20 cm oriented so that its faces are
parallel to the co-ordinate planes?
29. Careful measurement of the electric field at the surface of a [2]
black box indicates that the net outward flux through the surface
 of the box is 8.0 × 103 N m2 C-1.
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?
30. A point charge +10μC is a distance 5 cm directly above the [3]
center 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)

31. A point charge of 2.0 μC is at the centre of a cubic Gaussian [1]

surface 9.0 cm on edge. What is the net electric flux through the
surface?

32. A point charge causes an electric flux of −1.0 × 10 N m /C to

3 2 [2]
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?
33. A conducting sphere of radius 10 cm has an unknown charge. If [2]
the electric field, 20 cm from the centre of the sphere is
1.5 × 10 N /C and points radially inward, what is the net charge
3

on the sphere?
34. A uniformly charged conducting sphere of 2.4 m diameter has a [2]
surface charge density of 80.0 μCm-2.
a. Find the charge on the sphere.
b. What is the total electric flux leaving the surface of the
sphere?

35. An infinite line charge produces a field of 9 × 104 NC-1 at [1]

distance of 2 cm. Calculate the linear charge density.
36. Two large, thin metal plates are parallel and close to each other. [3]
On their inner faces, the plates have surface charge densities of
opposite signs and of magnitude 17.0 × 10-22 C/m2. 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?
37. It is now believed that protons and neutrons (which constitute [3]
nuclei of ordinary matter) are themselves built out of more
elementary units called quarks. A proton and a neutron consists
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 , 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 a neutron.