Recommended MCQs - 80 Questions - Electric Charges
Contact Number: 9667591930 / 8527521718
and Fields
Q1. A charge q is to be divided into two small conducting
spheres. What should be the value of charges on the
spheres so that when placed at a certain distance apart, the
repulsive force between them is maximum?
(1) and
q
4
q
(2)
2
q
(3)
3
q
3q
and
and
4
q
2
q
Q6. Two charges +2 C and +6 C are repelling each other
with a force of 12 N. If each charge is given –2 C of
charge, then the value of the force will be:
(1) 4 N (Attractive)
(2) 4 N (Repulsive)
(3) 8 N (Repulsive)
(4) Zero
3
q
Q7. If 109 electrons move out of a body to another body
every second, how much time approximately is required to
19
Q2. When 10 electrons are removed from a neutral get a total charge of 1 C on the other body?
1. 200 years
metal plate, the electric charge on it is?
2. 100 years
(1) –1.6 C
3. 150 years
(2) +1.6 C
4. 250 years
(3) 10+19 C
(4) 10–19 C
Q8. The acceleration of an electron due to the mutual
attraction between the electron and a proton when they
Q3. Two positive ions, each carrying a charge q, are
are 1. 6 A apart is,
separated by a distance d. If F is the force of repulsion
kg, e = 1. 6 × 10
C)
between the ions, the number of electrons missing from (m ≃ 9 × 10
each ion will be:
(T ake
= 9 × 10 N m C
)
(e is the charge on an electron)
1. 10 m/s
1.
2. 10 m/s
3. 10 m/s
2. √
4. 10 m/s
3. √
Q9. Four charges are arranged at the corners of a square
4.
ABCD as shown in the figure. The force on a positive
charge kept at the center of the square is
(4)
4
and
4
o
−31
−19
e
1
9
2
−2
4πε0
4πε0 F d
e
2
23
2
22
2
25
2
2
4πε0 F d
d
e
4πε0 F d
2
2
4πε0 F d
q
24
2
2
2
2
2
Q4. Two charges 2 μC and 8μC are separated by 6 cm.
The neutral point is at:
1. 4 cm from 2 μC.
2. 2 cm from 2 μC.
3. 2 cm from 8 μC.
4. 3 cm from 8 μC.
Q5. A polythene piece rubbed with wool is found to have
a negative charge of 3 × 10 C . Transfer of mass from 1. Zero
2. Along diagonal AC
wool to polythene is:
3. Along diagonal BD
(1) 0. 7 × 10
kg
4. Perpendicular to the side AB
−7
−18
(2)
(3)
1. 7 × 10
0. 7 × 10
(4) 1. 7 × 10
−17
−17
−18
kg
kg
kg
Q10. Two point charges A and B, having charges +Q and Q respectively, are placed at certain distance apart and
force acting between them is F. If 25% charge of A is
transferred to B, then force between the charges becomes:
1.
2. F
3.
4F
3
9F
16
4.
16F
9
Page: 1
Recommended MCQs - 80 Questions - Electric Charges
Contact Number: 9667591930 / 8527521718
and Fields
Q11. Three charges are placed at the vertices of an
equilateral triangle of side ‘a’ as shown in the following
figure. The force experienced by the charge placed at the
vertex A in a direction normal to BC is:
Q15. When 2 point charges +q and +3q held at a distance
r from each other are released, they have an acceleration
of a and 2a respectively. When we distribute the total
charge equally between them, keep them at same distance
as the original and release them, their accelerations now
would be:
1. 2a and 4a
2.
and
4a
8a
3
(1) Q /(4πε a )
(2) −Q /(4πε a
(3) Zero
(4) Q /(2πε a )
2
2
0
2
2
0
2
)
3.
9a
4.
2a
4
3
3
and
and
9a
2
4a
3
Q16. Four charges are arranged at the corners of a square
ABCD, as shown in the adjoining figure. The force on the
charge kept at the centre O is
2
0
Q12. The force between two charges 0.06 m apart is 5 N.
If each charge is moved towards the other by 0.01 m, then
the force between them will become:
(1) 7.20 N
(2) 11.25 N
(3) 22.50 N
(4) 45.00 N
(1) Zero
(2) Along the diagonal AC
Q13. Five balls numbered 1 to 5 are suspended using (3) Along the diagonal BD
separate threads. Pairs (1, 2), (2, 4), and (4, 1) show (4) Perpendicular to side AB
electrostatic attraction, while pairs (2, 3) and (4, 5) show
repulsion. Therefore ball 1 must be:
Q17. If a soap bubble is given some charge, then its
(1) positively charged.
radius:
(2) negatively charged.
1. increases.
(3) neutral.
2. decreases.
(4) made of metal.
3. remain unchanged.
4. may increase or decrease depending upon whether the
Q14. Two small spheres each having the charge +Q are given charge is positive or negative.
suspended by insulating threads of length L from a hook.
This arrangement is taken in space where there is no Q18. An infinite number of charges, each of charge 1 μC,
gravitational effect, then the angle between the two are placed on the x-axis with co-ordinates x = 1, 2, 4, 8,
suspensions and the tension in each will be:
....∞. If a charge of 1 C is kept at the origin, then what is
the net force acting on 1 C charge?
(1) 180 ,
(1) 9000 N
(2) 12000 N
(2) 90 ,
(3) 24000 N
(3) 180 ,
(4) 36000 N
Q
(2L)
Q
1
o
4πε0
o
(4) 180
o
,
2
1
4πε0
o
L
2
2
2
2
1
Q
4πε0
2L
1
Q
4πε0
L
2
2
2
Page: 2
Recommended MCQs - 80 Questions - Electric Charges
Contact Number: 9667591930 / 8527521718
and Fields
Q19. Two spherical conductors B and C having equal radii
and carrying equal charges in them repel each other with a
force F when kept apart at some distance. A third
spherical conductor having same radius as that of B but
uncharged is brought in contact with B, then brought in
contact with C and finally removed away from both. The
new force of repulsion between B and C is
(1) F/4
(2) 3 F/4
(3) F/8
(4) 3 F/8
Q23. A large non-conducting sheet S is given a uniform
charge density. Two uncharged small, metal rods A and B
are placed near the sheet as shown in the following
diagram. Then the incorrect option is:
Q20. An electron is moving around the nucleus of a 1. S attracts A.
hydrogen atom in a circular orbit of radius r. The 2. S attracts B.
→
3. A attracts B.
Coulomb force F on electron is (Where K =
)
4. S repels A.
1
4πε0
(1) −K
e
2
r̂
Q24. Two equal negative charge – q is fixed at the fixed
points (0, a) and (0, –a) on the Y-axis. A positive charge Q
→
is released from rest at the point (2a, 0) on the X-axis. The
(3) −K r
charge Q will:
(4) K r̂
(1) execute simple harmonic motion about the origin.
(2) move to the origin and remain at rest.
Q21. Suppose the charge of a proton and an electron differ (3) move to infinity.
slightly. One of them is –e, the other is (e+ Δe). If the net (4) execute the oscillatory but not simple harmonic
of electrostatic force and gravitational force between two motion.
hydrogen atoms placed at a distance d (much greater than
atomic size) apart is zero, then Δe is of the order of? Q25. The unit of permittivity of free space ε0 is :[Given mass of hydrogen m = 1. 67 × 10
kg]
(1) Newton metre2 / Coulomb2
(2) Coulomb2 /Newton metre2
1. 10
C
(3) Coulomb2/ (Newton metre)2
(4) Coulomb/Newton metre
2. 10
C
(2) K
e
r
r
2
3
→
r
3
e
r
e
r
2
3
2
2
−27
h
−23
−37
3. 10
−47
4. 10
−20
C
C
Q26. A total charge Q is broken in two parts Q1 and Q2
and they are placed at a distance R from each other. The
maximum force of repulsion between them will occur,
when:
(1) Q
(2) Q
(3) Q
Q22. The charge on 500 cc of water due to protons will
(4) Q
be:
(1) 6.0 × 1027 C
(2) 2.67 × 107 C
(3) 6 × 1023 C
(4) 1.67 × 1023 C
2
2
2
1
=
=
=
=
Q
R
Q
4
Q
4
Q
2
, Q1 = Q −
, Q1 = Q −
, Q1 =
, Q2 =
Q
R
2Q
3
3Q
4
Q
2
Page: 3
Recommended MCQs - 80 Questions - Electric Charges
Contact Number: 9667591930 / 8527521718
and Fields
Q27. A thin conducting ring of radius R is given a charge
+Q. The electric field at the centre O of the ring due to the
charge on the part AKB of the ring is E. The electric field
at the centre due to the charge on the part ACDB of the
ring is
Q30. The electrostatic field due to a charged conductor
just outside the conductor is
1. zero and parallel to the surface at every point inside the
conductor
2. zero and is normal to the surface at every point inside
the conductor
3. parallel to the surface at every point and zero inside the
conductor
4. normal to the surface at every point and zero inside the
conductor
Q31. The figure shows the electric lines of force emerging
from a charged body. If the electric field at A and B are EA
and EB respectively and if the displacement between A
and B is r, then:
1. 3E along KO
2. E along OK
3. f along KO
4. 3 E along OK
Q28. A charged particle q of mass m is released on the y→
axis at y = a in an electric field E =
of particle on reaching origin will be:
1.
2.
3.
4.
√
ˆ
− 4y j
. The speed
2a
mq
a
√mq
2a√
2√
q
m
a
mq
(1) EA > EB
(2) EA < EB
(3) E
=
(4) E
=
A
A
EB
r
EB
r
2
Q29. Three identical positive point charges, as shown are
placed at the vertices of an isosceles right angled triangle. Q32. Three infinitely long charge sheets are placed as
Which of the numbered vectors coincides in direction with shown in the figure. The electric field at point P is:
the electric field at the mid-point M of the hypotenuse
(1) 1
(2) 2
(3) 3
(4) 4
(1)
2σ
εo
(2) −
(3)
4σ
εo
(4) −
ˆ
k
2σ
εo
ˆ
k
ˆ
k
4σ
εo
ˆ
k
Page: 4
Recommended MCQs - 80 Questions - Electric Charges
Contact Number: 9667591930 / 8527521718
and Fields
Q33. Which of the following graphs shows the variation
of electric field E due to a hollow spherical conductor of
radius R as a function of distance from the centre of the
sphere?
Q35. A spherical conductor of radius 10 cm has a charge
of 3.2 x 10
C distributed uniformly. What is the
magnitude of the electric field at a point 15 cm from the
center of the sphere?
−7
(
(1)
1
4π∈0
=
9 × 10
1. 1.28 x 10
2. 1.28 x 10
3. 1.28 x 10
4. 1.28 x 10
5
6
7
4
9
2
2
N m /C )
N/C
N/C
N/C
N/C
Q36. A metallic solid sphere is placed in a uniform
electric field. The lines of force follow the path(s) shown
in figure as
(2)
(3)
(1) 1
(2) 2
(3) 3
(4) 4
Q37. Three positive charges of equal value q are placed at
the vertices of an equilateral triangle. The resulting lines
of force should be sketched as in
(4)
Q34. In the following four situations, charged particles are
at an equal distance from the origin. Arrange the (1)
magnitude of the net electric field at origin, greatest first.
(2)
(3)
(4)
Q38. A toy car with charge q moves on a frictionless
horizontal plane surface under the influence of a uniform
→
1. (i) > (ii) > (iii) > (iv)
2. (ii) > (i) > (iii) > (iv)
3. (i) > (iii) > (ii) > (iv)
4. (iv) > (iii) > (ii) > (i)
→
electric field E . Due to the force q E , its velocity
increases from 0 to 6 m/s in one-second duration. At that
instant, the direction of the field is reversed. The car
continues to move for two more seconds under the
influence of this field. The average velocity and the
average speed of the toy car between 0 to 3 seconds are
respectively:1. 2 m/s, 4 m/s
2. 1 m/s, 3 m/s
3. 1 m/s, 3.5 m/s
4. 1.5 m/s, 3 m/s
Page: 5
Recommended MCQs - 80 Questions - Electric Charges
Contact Number: 9667591930 / 8527521718
and Fields
Q39. A charged ball B hangs from a silk thread S, which
makes an angle θ with a large charged conducting sheet P,
as shown in the figure. The surface charge density σ of the
sheet is proportional to
Q43. An infinite number of electric charges each equal to
5 nano-coulomb (magnitude) are placed along x-axis at x
= 1 cm, x = 2 cm, x = 4 cm, x = 8 cm ………. and so on. In
the setup if the consecutive charges have opposite sign,
then the electric field in Newton/Coulomb at x = 0 is
(
1
9
4πε0
2
2
= 9 × 10 N − m /c )
(1) 12 × 104
(2) 24 × 104
(3) 36 × 104
(4) 48 × 104
Q44. Two identical conductors of copper and aluminium
are placed in an identical electric field. The magnitude of
induced charge in the aluminum will be
(1) Zero
(2) Greater than in copper
(3) Equal to that in copper
(4) Less than in copper
(1) sin θ
(2) tan θ
(3) cos θ
(4) cot θ
Q40. An electron falls from rest through a vertical
distance h in a uniform and vertically upward-directed
electric field E. The direction of the electric field is now
reversed, keeping its magnitude the same. A proton is
allowed to fall from rest through the same vertical
distance h. The fall time of the electron in comparison to
the fall time of the proton is:
1. smaller.
2. 5 times greater.
3. 10 times greater.
4. equal.
Q45. Two parallel infinite line charges with linear charge
densities +λ C/m and + λ C/m are placed at a
distance R. The electric field mid-way between the two
line charges is:
1.
N /C
λ
2πε0 R
2. zero
3.
N /C
2λ
πε0 R
4.
λ
πε0 R
N /C
Q41. A particle of mass m and carrying charge -q1 is Q46. An electron enters an electric field with its velocity
moving around a charge +q2 along a circular path of in the direction of the electric lines of force. Then:
(1) the path of the electron will be a circle.
radius r. The period of revolution of the charge -q1 is:
(2) the path of the electron will be a parabola.
(3) the velocity of the electron will decrease.
√
1.
(4) the velocity of the electron will increase.
2. √
Q47. The electric field at a distance
from the centre of
3. √
a charged conducting spherical shell of radius R is E. The
4. zero
electric field at a distance
from the centre of the sphere
Q42. Two-point charges +8q and –2q are located at x = 0 is:
and x = L respectively. The location of a point on the x- 1. E
axis at which the net electric field due to these two point 2.
charges is zero is
3.
(1) 8 L
4. Zero
(2) 4 L
(3) 2 L
(4)
3
16π ε0 mr
3
q1 q2
3
8π ε0 mr
3
q1 q2
3R
q1 q2
3
16π ε0 mr
2
3
R
2
E
2
E
2
L
4
Page: 6
Recommended MCQs - 80 Questions - Electric Charges
Contact Number: 9667591930 / 8527521718
and Fields
Q48. A charge q is placed in an uniform electric field E. If Q53. The ratio of the electric flux linked with shell A and
it is released, then the K.E of the charge after travelling shell B in the diagram shown below isdistance y will be :
1. qEy
2. 2qEy
3.
qEy
2
4. √qEy
Q49. In millikan oil drop experiment a charged drop falls
with a terminal velocity v. If an electric field E is applied
vertically upwards it moves with terminal velocity 2v in
upward direction. If electric field reduces to E/2 then its
terminal velocity will be 1. v/2
2. v
3.
4. 2v
3v
2
1.
2.
3.
4.
1: 1
1: 2
1: 4
4: 2
Q54. What is the flux through a cube of side a, if a point
charge of q is placed at one of its corners?
1.
2q
εo
Q50. A hollow metal sphere of radius R is uniformly
charged. The electric field due to the sphere at a distance r
from the centre:
1. decreases as r increases for r < R and for r > R.
2. increases as r increases for r < R and for r > R.
3. zero as r increases for r < R, decreases as r increases for
r > R.
4. zero as r increases for r < R, increases as r increases for
r > R.
2.
3.
4.
q
8εo
q
εo
q
2εo
Q55. A point charge is placed at the center of the spherical
Gaussian surface. The electric flux through the surface is
changed if the:
1. sphere is replaced by a cube of the same volume.
2. sphere is replaced by a cube of half volume.
Q51. Point charges +4q, –q and +4q are kept on the x-axis 3. charge is moved off-centre in the original sphere.
at points x = 0, x = a and x = 2a respectively, then :4. charge is moved just outside the original sphere.
1. Only q is in stable equilibrium.
2. None of the charges are in equilibrium.
Q56. A square surface of side L (m) is in the plane of the
3. All the charges are in unstable equilibrium.
paper. A uniform electric field E→ (V/m), also in the plane
4. All the charges are in stable equilibrium.
of the paper, is limited only to the lower half of the square
surface, (see figure). The electric flux in SI units
Q52.
associated
with
the
surface
is:
A charge Q is enclosed by a Gaussian spherical surface of
radius R. If the radius is doubled, then the outward electric
flux will
1. be reduced to half
2. remain the same
3. be doubled
1. EL /(2ε
2. EL /2
3. zero
4. EL
2
4. increased four times
0)
2
2
Page: 7
Recommended MCQs - 80 Questions - Electric Charges
Contact Number: 9667591930 / 8527521718
and Fields
Q57. An electric dipole is placed at the centre of a sphere.
Which of the following is correct?
1. The electric flux through the sphere is zero.
2. The electric field is zero at every point on the sphere.
3. The electric field is zero at every point inside the
sphere.
4. The electric field is uniform inside the sphere.
Q60. The electric field in a certain region is acting radially
outward and is given by E = Ar. A charge contained in a
sphere of radius 'a' centered at the origin of the field will
be given by:
1. 4πεo Aa
2. εo Aa
2
3. 4πεo Aa
Q58. A point charge q is placed at the center of the open
face of a hemispherical surface as shown in the figure.
The flux linked with the surface is:
4. εo Aa
2
3
3
Q61. The electric flux from a cube of edge l is ϕ. What
will be its value if the edge of the cube is made 2l and the
charge enclosed is halved?
1. ϕ
2. 2ϕ
3. 4ϕ
4. ϕ
1
2
1. zero
2.
q
2ε0
3.
4.
Q62. Refer to the arrangement of charges in the figure and
a Gaussian surface of radius R with Q at the centre. Then
q
ε0
qπr
2
Q59. A hollow cylinder has a charge q coulomb within
it(at the geometrical centre). If ϕ is the electric flux in unit
of Volt-meter associated with the curved surface B, the
flux linked with the plane surface A in unit of Volt-meter
will be:
(a) total flux through the surface of the sphere is
1.
2.
3.
4.
1
2
(
q
ε0
− Φ)
q
2ε0
Φ
3
q
ε0
− Φ
(b) field on the surface of the sphere is
−Q
4πε0 R
2
−Q
ε0
.
.
(c) flux through the surface of the sphere due to 5Q is
zero.
(d) field on the surface of the sphere due to -2Q is the
same everywhere.
(1) (a, d)
(2) (a, c)
(3) (b, d)
(4) (c, d)
Page: 8
Recommended MCQs - 80 Questions - Electric Charges
Contact Number: 9667591930 / 8527521718
and Fields
Q63. If there were only one type of charge in the universe,
then,
(a) ∮ E. dS ≠ 0 on any surface.
(b) ∮ E. dS = 0 if the charge is outside the surface.
(c) ∮ E. dS could not be defined.
(d) ∮ E. dS =
if charges of magnitude q were inside
the surface.
(1) (a, d)
(2) (a, c)
(3) (b, d)
(4) (c, d)
Q66.
Q64. An isolated sphere of radius R contains a uniform
volume distribution of positive charge. Which of the curve
on the graph below correctly illustrates the dependence of
the magnitude of the electric field of the sphere as a
function of the distance r from its centre?
(4)
s
s
s
q
s
A spherical conducting shell of inner radius r and outer
radius r has a charge Q. A charge q is placed at the center
of the shell. The surface charge density on the outer
surfaces of the shell is:
1
2
ε0
(1)
(2)
Q+q
4πr2
2
q
4πr1
2
− ( Q+q )
(3)
4πr2
2
−q
4πr1
2
Q67. Consider the charge configuration and spherical
Gaussian surface as shown in the figure. When calculating
the flux of the electric field over the spherical surface, the
electric field will be due to:
1. A
2. B
3. C
4. D
(1) q2.
Q65. A point charge q is placed at a distance a/2 directly (2) only the positive charges.
above the centre of a square of side a. The electric flux (3) all the charges.
through the square is
(4) +q1 and – q1.
(1)
q
ε0
(2)
(3)
(4)
q
πε0
q
4ε0
q
6ε0
Q68. X and Y are large, parallel conducting plates close to
each other. Each face has an area A. X is given a charge
Q. Y is without any charge. Point A, B, and C are as
shown in the figure. The incorrect option is:
1. the field at B is
2. the field at B is
Q
2ε0 A
Q
ε0 A
3. the fields at A, B and C are of the same magnitude
4. the fields at A and C are of the same magnitude but in
opposite directions
Page: 9
Recommended MCQs - 80 Questions - Electric Charges
Contact Number: 9667591930 / 8527521718
and Fields
Q69. Consider a region inside which there are various Q73. In a certain region of space, the electric field is along
types of charges but the total charge is zero. At points the z-direction throughout. The magnitude of the electric
outside the region,
field is, however, not constant but increases uniformly
along the positive z-direction, at the rate of 10 N C
(a) the electric field is necessarily zero.
per meter. What is the torque experienced by a system
(b) the electric field is due to the dipole moment of the having a total dipole moment equal to 10 C m in the
charge distribution only.
negative z-direction?
(c) the dominant electric field is ∝ , for large r, where r (1) 10 N m
(2) 0
is the distance from the origin in this region.
(d) the work done to move a charged particle along a (3) 10 N m
(4) 0. 01 N m
closed path, away from the region, will be zero.
(1) (b, d)
(2) (a, c)
Q74. An electric dipole is kept in a uniform electric field
(3) (b, d)
such that the dipole moment is not collinear with the
(4) (c, d)
electric field. It experiences:
Q70. An electric dipole is placed at an angle of 30 ° with 1. a force and torque.
an electric field intensity 2 x 105 N/C. It experiences a 2. a force but no torque.
torque equal to 4 Nm. The charge on the dipole, if the 3. a torque but no force.
4. neither a force nor a torque.
dipole length is 2 cm, is
5
−1
−7
1
r
−2
3
−1
1. 8 mC
2. 2 mC
3. 5 mC
4. 7 μC
Q71. Three-point charges + q and -2q and +q are placed at
points (x=0, y=a, z=0), (x=0, y=0, z=0) and
(x=a, y=0, z=0), respectively. The magnitude and direction
of the electric dipole moment vector of this charge
assembly are:
1. √2qa along +y direction
2. √2qa along the line joining points (x=0, y= 0, z=0)
And (x=a, y=a, z=0)
3. qa along the line joining points (x=0, y=0, z=0) And
(x=a, y=a, z=0)
4. √2qa along +x direction
Q75. The electric field at a point on the equatorial plane at
a distance r from the centre of a dipole having dipole
→
moment P is given by:
(r>> separation of two charges forming the dipole,
= permittivity of free space )
1.
2.
3.
4.
→
→
E
P
=
4π ε0 r
=
2P
4π ε0 r
→
E
=
−
→
E
3
→
→
E
ε0
=
−
3
→
P
4π ε0 r
2
→
P
4π ε0 r
3
Q72. The net dipole moment of the system is of the
magnitude:
1.
2.
3.
4.
q × 2a
2q × 2a
q×a
2 × (2q × 2a)
Page: 10
Recommended MCQs - 80 Questions - Electric Charges
Contact Number: 9667591930 / 8527521718
and Fields
Q76. An electric dipole is kept at the origin as shown in Q79. The figure shows electric field lines in which an
the diagram. The point A, B, C are on a circular arc with electric dipole p is placed as shown. Which of the
the centre of curvature at the origin. If the electric fields at following statements is correct?
−
→
A, B and C respectively are E ,
the following is incorrect? (d>>l)
1
−
→
−
→
E2 , E3
, then which of
(1) The dipole will not experience any force.
(2) The dipole will experience a force towards the right.
(3) The dipole will experience a force towards the left.
(4) The dipole will experience a force upwards.
1.
2.
3.
4.
−
→
E1
−
→
=
− E3
=
− 2E2
−
→
E1
−
→
−
→
E1
−
→
=
E3
−
→
E3
Q80. The electric field at the equator of a dipole is E. If
the strength of the dipole and distance is now doubled
then the electric field will be :
1. E/2
2. E/8
3. E/4
4. E
−
−
→
=
− 2E2
Q77. Two-point charges +q and –q are held fixed at (–d,
0) and (d, 0) respectively of an (x, y) coordinate system.
Then:
(1) E at all points on the y-axis is along ˆi .
→
(2) The electric field E at all points on the x-axis has the
same direction.
(3) Dipole moment is 2qd directed along ˆi .
(4) Work has to be done in bringing a test charge from
infinity to the origin.
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→
Q78. Two point dipoles of dipole moment →
p
and p are
1
at a distance x from each other and
between the dipole is :
1.
2.
3.
4.
1
4πε0
1
4πε0
1
4πε0
1
4πε0
4p1 p2
x
4
3p1 p2
x
3
6p1 p2
x
4
8p1 p2
x
4
→ ∣∣→
p
p
1 ∣∣
2
Answers
2
. The force
1.
7.
13.
19.
25.
31.
37.
43.
49.
55.
61.
67.
73.
79.
(2)
(1)
(3)
(4)
(2)
(1)
(3)
(3)
(1)
(4)
(1)
(3)
(2)
(3)
2.
8.
14.
20.
26.
32.
38.
44.
50.
56.
62.
68.
74.
80.
(2)
(3)
(1)
(3)
(4)
(2)
(2)
(3)
(3)
(3)
(2)
(2)
(3)
(3)
3.
9.
15.
21.
27.
33.
39.
45.
51.
57.
63.
69.
75.
(3)
(4)
(2)
(2)
(2)
(1)
(2)
(2)
(3)
(1)
(3)
(4)
(4)
4.
10.
16.
22.
28.
34.
40.
46.
52.
58.
64.
70.
76.
(2)
(3)
(3)
(2)
(3)
(3)
(1)
(3)
(2)
(2)
(3)
(2)
(1)
5.
11.
17.
23.
29.
35.
41.
47.
53.
59.
65.
71.
77.
(4)
(3)
(1)
(4)
(2)
(1)
(1)
(4)
(1)
(1)
(4)
(2)
(1)
6.
12.
18.
24.
30.
36.
42.
48.
54.
60.
66.
72.
78.
(4)
(2)
(2)
(4)
(4)
(4)
(3)
(1)
(2)
(3)
(1)
(1)
(3)
Page: 11