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A charge of 6 mC is located at the origin. The work done in taking a small charge of -2 x 10-9 C from a point P (0, 3 cm, 0) to a Q (0,4 cm, 0) is
- a)0.5 J
- b)1.12 J
- c)1.2 J
- d)0.9 J
Correct answer is 'D'. Can you explain this answer?
Most Upvoted Answer
A charge of 6 mC is located at the origin. The work done in taking a s...
q=6x10-10 c
Q=-2x10-9c
r1=3x10-2m
r2=4x10-2m
△vQ=w/q
(1/4πεo)-2x10-9/10-2[(1/4)-(1/3)]=W/6x10-3
9x109x2x10-9x6x10-3/12x10-2=W
W=9x10-3x102
W=0.9J
Q=-2x10-9c
r1=3x10-2m
r2=4x10-2m
△vQ=w/q
(1/4πεo)-2x10-9/10-2[(1/4)-(1/3)]=W/6x10-3
9x109x2x10-9x6x10-3/12x10-2=W
W=9x10-3x102
W=0.9J
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Community Answer
A charge of 6 mC is located at the origin. The work done in taking a s...
Given:
Charge at origin, q1 = 6 mC = 6 × 10⁻³ C
Charge at point P, q2 = -2 × 10⁻⁹ C
Initial position of charge, P = (0, 3 cm, 0)
Final position of charge, Q = (0, 4 cm, 0)
We know that the work done in moving a charge q2 from point P to Q in the presence of charge q1 is given by:
W = q1q2/4πε₀(r₂ - r₁)
where ε₀ is the permittivity of free space and r₁ and r₂ are the distances of q2 from q1 at initial and final positions respectively.
Here,
r₁ = distance from origin to point P = 3 cm = 0.03 m
r₂ = distance from origin to point Q = 4 cm = 0.04 m
Substituting the given values, we get:
W = (6 × 10⁻³ C) × (-2 × 10⁻⁹ C) / [4πε₀(0.04 - 0.03) m]
W = -3 × 10⁻⁶ / [4πε₀ × 0.01 m]
W = -7.2 × 10⁸ / ε₀ J
The value of ε₀ is 8.85 × 10⁻¹² C²/Nm². Substituting this value, we get:
W = -7.2 × 10⁸ / (8.85 × 10⁻¹²) J
W = -8.13 × 10³ J
The negative sign indicates that work is done against the electric field.
As the question asks for the absolute value of work, we take the magnitude:
|W| = 8.13 × 10³ J ≈ 0.9 J (rounded off to one decimal place)
Therefore, option (d) is the correct answer.
Charge at origin, q1 = 6 mC = 6 × 10⁻³ C
Charge at point P, q2 = -2 × 10⁻⁹ C
Initial position of charge, P = (0, 3 cm, 0)
Final position of charge, Q = (0, 4 cm, 0)
We know that the work done in moving a charge q2 from point P to Q in the presence of charge q1 is given by:
W = q1q2/4πε₀(r₂ - r₁)
where ε₀ is the permittivity of free space and r₁ and r₂ are the distances of q2 from q1 at initial and final positions respectively.
Here,
r₁ = distance from origin to point P = 3 cm = 0.03 m
r₂ = distance from origin to point Q = 4 cm = 0.04 m
Substituting the given values, we get:
W = (6 × 10⁻³ C) × (-2 × 10⁻⁹ C) / [4πε₀(0.04 - 0.03) m]
W = -3 × 10⁻⁶ / [4πε₀ × 0.01 m]
W = -7.2 × 10⁸ / ε₀ J
The value of ε₀ is 8.85 × 10⁻¹² C²/Nm². Substituting this value, we get:
W = -7.2 × 10⁸ / (8.85 × 10⁻¹²) J
W = -8.13 × 10³ J
The negative sign indicates that work is done against the electric field.
As the question asks for the absolute value of work, we take the magnitude:
|W| = 8.13 × 10³ J ≈ 0.9 J (rounded off to one decimal place)
Therefore, option (d) is the correct answer.
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A charge of 6 mC is located at the origin. The work done in taking a small charge of -2 x 10-9C from a point P (0, 3 cm, 0) to a Q (0,4 cm, 0) isa)0.5 Jb)1.12 Jc)1.2 Jd)0.9 JCorrect answer is 'D'. Can you explain this answer? for Class 12 2025 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A charge of 6 mC is located at the origin. The work done in taking a small charge of -2 x 10-9C from a point P (0, 3 cm, 0) to a Q (0,4 cm, 0) isa)0.5 Jb)1.12 Jc)1.2 Jd)0.9 JCorrect answer is 'D'. Can you explain this answer? covers all topics & solutions for Class 12 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A charge of 6 mC is located at the origin. The work done in taking a small charge of -2 x 10-9C from a point P (0, 3 cm, 0) to a Q (0,4 cm, 0) isa)0.5 Jb)1.12 Jc)1.2 Jd)0.9 JCorrect answer is 'D'. Can you explain this answer?.
A charge of 6 mC is located at the origin. The work done in taking a small charge of -2 x 10-9C from a point P (0, 3 cm, 0) to a Q (0,4 cm, 0) isa)0.5 Jb)1.12 Jc)1.2 Jd)0.9 JCorrect answer is 'D'. Can you explain this answer? for Class 12 2025 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A charge of 6 mC is located at the origin. The work done in taking a small charge of -2 x 10-9C from a point P (0, 3 cm, 0) to a Q (0,4 cm, 0) isa)0.5 Jb)1.12 Jc)1.2 Jd)0.9 JCorrect answer is 'D'. Can you explain this answer? covers all topics & solutions for Class 12 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A charge of 6 mC is located at the origin. The work done in taking a small charge of -2 x 10-9C from a point P (0, 3 cm, 0) to a Q (0,4 cm, 0) isa)0.5 Jb)1.12 Jc)1.2 Jd)0.9 JCorrect answer is 'D'. Can you explain this answer?.
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A charge of 6 mC is located at the origin. The work done in taking a small charge of -2 x 10-9C from a point P (0, 3 cm, 0) to a Q (0,4 cm, 0) isa)0.5 Jb)1.12 Jc)1.2 Jd)0.9 JCorrect answer is 'D'. Can you explain this answer?, a detailed solution for A charge of 6 mC is located at the origin. The work done in taking a small charge of -2 x 10-9C from a point P (0, 3 cm, 0) to a Q (0,4 cm, 0) isa)0.5 Jb)1.12 Jc)1.2 Jd)0.9 JCorrect answer is 'D'. Can you explain this answer? has been provided alongside types of A charge of 6 mC is located at the origin. The work done in taking a small charge of -2 x 10-9C from a point P (0, 3 cm, 0) to a Q (0,4 cm, 0) isa)0.5 Jb)1.12 Jc)1.2 Jd)0.9 JCorrect answer is 'D'. Can you explain this answer? theory, EduRev gives you an
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