KKMishra's Tutorials: H C Verma solutions, ELECTRIC FIELD AND POTENTIAL, EXERCISES, Q71 to Q75, Chapter-29, Concepts of Physics, Part-II

Electric Field and Potential

EXERCISES, Q71 to Q75

71. Two particles A and B, having opposite charges 2.0x10⁻⁶ C and -2.0x10⁻⁶ C, are placed at a separation of 1.0 cm. (a) Write down the electric dipole moment of this pair. (b) Calculate the electric field at a point on the axis of the dipole 1.0 m away from the center. (c) Calculate the electric field at a point on the perpendicular bisector of the dipole and 1.0 m away from the center.

Answer: (a) Given q = 2.0x10⁻⁶ C. d = 1.0 cm =0.01 m.

Hence the electric dipole moment of the pair,

p =qd

=2.0x10⁻⁶*0.01 C-m

=2.0x10⁻⁸ C-m.

(b) The electric field at a point on the dipole axis is given as,

E =2kp/r³, where r is the distance of the point from the center of the dipole.

=29x10⁹2.0x10⁻⁸/1³

=360 N/C. Along the axis.

(c) On the perpendicular bisector of a dipole, the electric field at a point is given as,

E =kp/r³

=9x10⁹*2.0x10⁻⁸/1³

=180 N/C. Along the antiparallel to the dipole axis.

72. Three charges are arranged on the vertices of an equilateral triangle as shown in the figure (29-E6). Find the dipole moment of the combination.
The figure for Q-72

Answer: ABC is an equilateral triangle. At A, there is 2q charge while at B and C there is -q charge each. It can be assumed that there are two dipoles along AB and AC. The dipole moment of AB =qd along BA, and that of AC =qd along CA.
The diagram for Q-72

The resultant of these two vectors is the dipole moment of the combination, its magnitude is,

p (resultant) = √{2(qd)²+2(qd)².cos 60°}

=√{3(qd)²}

=qd√3, along the angle bisector, at A and away from the triangle, as shown in the diagram.

73. Find the magnitude of the electric field at the point P in the configuration shown in the (29-E7) for d>>a. Take 2qa = p.
The figure for Q-73

Answer: (a) The magnitude of electric field at P =kq/d²

=q/4πεₒd².

(b) The two charges q and -q are equivalent to a dipole with separation r=2a. Its dipole moment, p =q*2a =2aq

P is at the perpendicular bisector of the dipole. Hence the magnitude of the electric field here,

E =kp/d³

=(1/4πεₒ)p/d³

=p/4πεₒd³.

(c) Here we take the charges q and -q separated at 2a distance apart as a dipole. Its dipole moment, p=2aq. Point P is at the perpendicular bisector of this dipole and as in (b) above the magnitude of the electric field at P due to this dipole, E = p/4πεₒd³. Its direction is horizontal.

The electric field at point P due to the middle charge q,

E' =q/4πεₒd². Directed vertically upward. So the electric fields E and E' are mutually perpendicular. Hence the magnitude of the resultant electric field =√(E²+E'²)

=(1/4πεₒd²)√(q²+p²/d²)

=(1/4πεₒd³)√(q²d²+p²).

74. Two particles carrying charges -q and +q and having equal masses m each, are fixed at the ends of a light rod of length a to form a dipole. The rod is clamped at one end and is placed in a uniform electric field E with the axis of the dipole along the electric field. The rod is slightly tilted and then released. Neglecting gravity, find the time period of small oscillations.

Answer: Neglecting gravity, the dipole may be assumed as a pendulum and the force on the pendulum, F =qE as shown in the diagram.
Diagram for Q-74

The length of this pendulum = a.

Mass of the bob = m, hence

acceleration =F/m =qE/m.

The time period of a pendulum is,

T =2π√(l/g), here, l → a, and g →qE/m

So here time period is,

T =2π√{a/(qE/m)}

=2π√(ma/qE).

75. Assume that each atom in a copper wire contributes one free electron. Estimate the number of free electrons in a copper wire having a mass of 6.4 g (take the atomic weight of copper to be 64 g/mol).

Answer: Number of moles of copper in the given wire =6.4/64 =0.10 mole.

Number of atoms in 1 mole =6.02x10²³

{Avogadro's number}

Number of atoms in the wire that have 0.10 mole =6.02x10²²

Since one atom contributes one free electron, hence 6.02x10²² atoms will contribute 6.02x10²² free electrons.

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CHAPTER- 29- Electric Field and Potential

Questions for Short Answer

OBJECTIVE-I

OBJECTIVE -II

EXERCISES - Q1 - Q10

EXERCISES - Q11 - Q20

EXERCISES - Q21 - Q30

EXERCISES - Q31 - Q40

EXERCISES - Q41 - Q50

EXERCISES - Q51 - Q60

EXERCISES - Q61 - Q70

CHAPTER- 28- Heat Transfer

Questions for Short Answer

OBJECTIVE -I

OBJECTIVE - II

EXERCISES - Q1 to Q10

EXERCISES - Q11 to Q20

EXERCISES - Q21 to Q30

EXERCISES - Q31 to Q40

EXERCISES - Q41 to Q50

EXERCISES - Q51 to Q55

CHAPTER- 27-Specific Heat Capacities of Gases

Questions for Short Answer

OBJECTIVE - I

OBJECTIVE -II

EXERCISES - Q1 - Q10

EXERCISES - Q11 - Q20

EXERCISES - Q21 - Q30

EXERCISES - Q31 - Q35

CHAPTER- 26-Laws of Thermodynamics

Questions for Short Answer

OBJECTIVE - I

OBJECTIVE - II

EXERCISES - Q1 to Q10

EXERCISES - Q11 to Q22

CHAPTER- 25-CALORIMETRY

Questions for Short Answer

OBJECTIVE-I

OBJECTIVE-II

EXERCISES - Q1 to Q10

EXERCISES - Q-11 to Q-18

CHAPTER- 24-Kinetic Theory of Gases

Questions for Short Answer

OBJECTIVE - I

OBJECTIVE - II

EXERCISES- Q1 to 10

EXERCISES- Q11 to 20

EXERCISES- Q21 to 30

EXERCISES- Q31 to Q40

EXERCISES- Q41 to Q50

EXERCISES- Q51 to Q62

CHAPTER- 23 - Heat and Temperature

Questions for Short Answer

OBJECTIVE - I

OBJECTIVE - II

EXERCISES - Q-1 TO Q-10

EXERCISES - Q-11 TO Q-20

EXERCISES - Q-21 TO Q-34

CHAPTER- 22 - Photometry

Questions for Short Answer

OBJECTIVE - I

OBJECTIVE - II

EXERCISES

CHAPTER- 21 - Speed of Light

Questions for Short Answers

OBJECTIVE-I

OBJECTIVE-II

EXERCISES

CHAPTER- 20 - Dispersion and Spectra

Questions for Short Answers

OBJECTIVE-I

OBJECTIVE-II

EXERCISES

CHAPTER- 19 - Optical Instruments

Questions for Short Answers

OBJECTIVE-I

OBJECTIVE-II

EXERCISES - Q 1 to Q 12

EXERCISES - Q 13 to Q 24

CHAPTER- 18 - Geometrical Optics

Questions for Short Answers

OBJECTIVE-I

OBJECTIVE-II

EXERCISES - Q 1 to Q10

EXERCISES- Q11 to Q20

EXERCISES- Q21 to Q30

EXERCISES- Q31 to Q40

EXERCISES- Q41 to Q50

EXERCISES- Q51 to Q60

EXERCISES- Q61 to Q70

EXERCISES- Q71 TO 79

CHAPTER- 17 - Light Waves

Questions for Short Answers

OBJECTIVE - I

OBJECTIVE - II

EXERCISES - Q1-Q10

EXERCISES - Q11-Q20

EXERCISES - Q21-Q30

EXERCISES - Q31-Q41

CHAPTER- 16 - Sound Waves

Questions for Short Answers

OBJECTIVE-I

OBJECTIVE-II

EXERCISES - Q-1 TO Q-10

EXERCISES - Q-11 TO Q-20

EXERCISES -Q-21 TO Q-30

EXERCISES -Q-31 TO Q-40

EXERCISES -Q-41 TO Q-50

EXERCISES -Q-51 TO Q-60

EXERCISES -Q-61 TO Q-70

EXERCISES - Q-71 TO Q-80

EXERCISES - Q-81 TO Q-89

CHAPTER- 15 - Wave Motion and Waves on a String

Questions for Short Answers

OBJECTIVE-I

OBJECTIVE-II

EXERCISES - Q-1 TO Q-10

EXERCISES - Q-11 TO Q-20

EXERCISES - Q-21 TO Q-30

EXERCISES - Q-31 TO Q-40

EXERCISES - Q-41 TO Q-50

EXERCISES - Q-51 TO Q-57

CHAPTER- 14 - Fluid Mechanics

Questions for Short Answers

OBJECTIVE-I

OBJECTIVE-II

EXERCISES- Q-1 TO Q-10

EXERCISES- Q-11 TO Q-20

EXERCISES- Q-21 TO Q-32

CHAPTER- 13 - Fluid Mechanics

Questions for Short Answers

OBJECTIVE-I

OBJECTIVE-II

EXERCISES Q-1 TO Q-10

EXERCISES- Q11 TO Q20

EXERCISES Q-21 TO Q30

EXERCISES Q-31 TO Q35

CHAPTER- 12 - Simple Harmonic Motion

Questions for Short Answers

OBJECTIVE-I

OBJECTIVE-II

EXERCISES- Q1 TO Q10

EXERCISES- Q11 TO Q20

EXERCISES- Q21 TO Q30

EXERCISES- Q31 TO Q40

EXERCISES- Q41 TO Q50

EXERCISES- Q51 TO Q58 (2-Extra Questions)

CHAPTER- 11 - Gravitation

Questions for Short Answers

OBJECTIVE - I

OBJECTIVE - II

EXERCISES - Q_1 to Q_10

EXERCISES -Q-11 TO Q-20

EXERCISES -Q 21 TO 30

EXERCISES -Q 31 TO 39

CHAPTER- 10 - Rotational Mechanics

Questions for Short Answers

OBJECTIVE - I

OBJECTIVE - II

EXERCISES - Q-1 TO Q-15

EXERCISES - Q-16 TO Q-30

EXERCISES Q-31 TO Q-45

EXERCISES Q-46 TO Q-60

EXERCISES Q-61 TO Q-75

EXERCISES Q-76 TO Q-86

CHAPTER- 9 - Center of Mass, Linear Momentum, Collision

Questions for Short Answers

Objective - I

Objective - II

EXERCISES Q-1 TO Q-10

EXERCISES Q-11TO Q-20

EXERCISES Q-21 TO Q-30

EXERCISES Q-31 TO Q-42

EXERCISES Q-43 TO Q-54

CHAPTER- 8 - Work and Energy

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Click here for → Exercises (1-10)

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CHAPTER- 7 - Circular Motion

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CHAPTER- 6 - Friction

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For more practice on problems on friction solve these- "New Questions on Friction".

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CHAPTER- 5 - Newton's Laws of Motion

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Click here for→Newton's Laws of Motion,Exercises(Q.No. 28 to 42)
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CHAPTER- 4 - The Forces

The Forces-

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Monday, November 2, 2020

H C Verma solutions, ELECTRIC FIELD AND POTENTIAL, EXERCISES, Q71 to Q75, Chapter-29, Concepts of Physics, Part-II

Answer: (a) Given q = 2.0x10⁻⁶ C. d = 1.0 cm =0.01 m.

Hence the electric dipole moment of the pair,

p =qd

=2.0x10⁻⁶*0.01 C-m

=2.0x10⁻⁸ C-m.

(b) The electric field at a point on the dipole axis is given as,

E =2kp/r³, where r is the distance of the point from the center of the dipole.

=2*9x10⁹*2.0x10⁻⁸/1³

=360 N/C. Along the axis.

(c) On the perpendicular bisector of a dipole, the electric field at a point is given as,

E =kp/r³

=9x10⁹*2.0x10⁻⁸/1³

=180 N/C. Along the antiparallel to the dipole axis.

72. Three charges are arranged on the vertices of an equilateral triangle as shown in the figure (29-E6). Find the dipole moment of the combination. The figure for Q-72

Answer: ABC is an equilateral triangle. At A, there is 2q charge while at B and C there is -q charge each. It can be assumed that there are two dipoles along AB and AC. The dipole moment of AB =qd along BA, and that of AC =qd along CA.The diagram for Q-72

The resultant of these two vectors is the dipole moment of the combination, its magnitude is,

p (resultant) = √{2(qd)²+2(qd)².cos 60°}

=√{3(qd)²}

=qd√3, along the angle bisector, at A and away from the triangle, as shown in the diagram.

73. Find the magnitude of the electric field at the point P in the configuration shown in the (29-E7) for d>>a. Take 2qa = p. The figure for Q-73

Answer: (a) The magnitude of electric field at P =kq/d²

=q/4πεₒd².

(b) The two charges q and -q are equivalent to a dipole with separation r=2a. Its dipole moment, p =q*2a =2aq

P is at the perpendicular bisector of the dipole. Hence the magnitude of the electric field here,

E =kp/d³

=(1/4πεₒ)p/d³

=p/4πεₒd³.

(c) Here we take the charges q and -q separated at 2a distance apart as a dipole. Its dipole moment, p=2aq. Point P is at the perpendicular bisector of this dipole and as in (b) above the magnitude of the electric field at P due to this dipole, E = p/4πεₒd³. Its direction is horizontal.

The electric field at point P due to the middle charge q,

E' =q/4πεₒd². Directed vertically upward. So the electric fields E and E' are mutually perpendicular. Hence the magnitude of the resultant electric field =√(E²+E'²)

=(1/4πεₒd²)√(q²+p²/d²)

=(1/4πεₒd³)√(q²d²+p²).

Answer: Neglecting gravity, the dipole may be assumed as a pendulum and the force on the pendulum, F =qE as shown in the diagram.Diagram for Q-74

The length of this pendulum = a.

Mass of the bob = m, hence

acceleration =F/m =qE/m.

The time period of a pendulum is,

T =2π√(l/g), here, l → a, and g →qE/m

So here time period is,

T =2π√{a/(qE/m)}

=2π√(ma/qE).

75. Assume that each atom in a copper wire contributes one free electron. Estimate the number of free electrons in a copper wire having a mass of 6.4 g (take the atomic weight of copper to be 64 g/mol).

Answer: Number of moles of copper in the given wire =6.4/64 =0.10 mole.

Number of atoms in 1 mole =6.02x10²³

{Avogadro's number}

Number of atoms in the wire that have 0.10 mole =6.02x10²²

Since one atom contributes one free electron, hence 6.02x10²² atoms will contribute 6.02x10²² free electrons.

---------------------------------------------------

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Links to the Chapters

CHAPTER- 8 - Work and Energy

Click here for → Question for Short AnswersClick here for → OBJECTIVE-IClick here for → OBJECTIVE-IIClick here for → Exercises (1-10)

Click here for → Exercises (11-20)

Click here for → Exercises (21-30)Click here for → Exercises (31-42)Click here for → Exercise(43-54)

CHAPTER- 7 - Circular Motion

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Click here for → OBJECTIVE-IClick here for → Friction - OBJECTIVE-IIClick here for → EXERCISES (1-10)Click here for → Exercises (11-20)Click here for → EXERCISES (21-31)For more practice on problems on friction solve these- "New Questions on Friction".

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CHAPTER- 5 - Newton's Laws of Motion

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Click here for→ Newton's laws of motion - Objective - IClick here for → Newton's Laws of Motion - Objective -IIClick here for → Newton's Laws of Motion-Exercises(Q. No. 1 to 12)

Click here for→Newton's Laws of Motion,Exercises(Q.No. 13 to 27)

Click here for→Newton's Laws of Motion,Exercises(Q.No. 28 to 42)-------------------------------------------------------------------------------

CHAPTER- 4 - The Forces

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CHAPTER- 3 - Kinematics - Rest and Motion

=29x10⁹2.0x10⁻⁸/1³

72. Three charges are arranged on the vertices of an equilateral triangle as shown in the figure (29-E6). Find the dipole moment of the combination.
The figure for Q-72

Answer: ABC is an equilateral triangle. At A, there is 2q charge while at B and C there is -q charge each. It can be assumed that there are two dipoles along AB and AC. The dipole moment of AB =qd along BA, and that of AC =qd along CA.
The diagram for Q-72

73. Find the magnitude of the electric field at the point P in the configuration shown in the (29-E7) for d>>a. Take 2qa = p.
The figure for Q-73

Answer: Neglecting gravity, the dipole may be assumed as a pendulum and the force on the pendulum, F =qE as shown in the diagram.
Diagram for Q-74

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CHAPTER- 6 - Friction

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