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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...
Work done is given by the formula:
W = q * ΔV
where q is the charge and ΔV is the potential difference.
Given:
Charge (q) = -2 x 10^-9 C (negative because it is a negative charge)
Initial point P: (0, 3 cm, 0)
Final point Q: (0, 4 cm, 0)
To find the potential difference (ΔV), we need to find the electric field at point P and point Q.
Finding the Electric Field:
The electric field (E) at a point due to a charge (Q) is given by the formula:
E = k * (Q / r^2)
where k is the electrostatic constant (9 x 10^9 Nm^2/C^2) and r is the distance from the charge.
At point P:
Distance from the charge (r) = 3 cm = 0.03 m
Electric field (E) = k * (Q / r^2) = (9 x 10^9) * (6 x 10^-6) / (0.03)^2 = 6 N/C
At point Q:
Distance from the charge (r) = 4 cm = 0.04 m
Electric field (E) = k * (Q / r^2) = (9 x 10^9) * (6 x 10^-6) / (0.04)^2 = 3.375 N/C
Finding the Potential Difference (ΔV):
The potential difference (ΔV) between two points in an electric field is given by the formula:
ΔV = E * d
where E is the electric field and d is the distance between the two points.
In this case, the distance between point P and Q is 1 cm = 0.01 m.
ΔV = E * d = 3.375 N/C * 0.01 m = 0.03375 V
Finding the Work done (W):
Using the formula W = q * ΔV, we can now calculate the work done.
W = -2 x 10^-9 C * 0.03375 V = -6.75 x 10^-11 J
Since work is a scalar quantity, the negative sign indicates that work is done against the electric field.
To convert the value to positive, we take the magnitude:
W = 6.75 x 10^-11 J
Therefore, the work done in taking a small charge from point P to Q is approximately 0.9 J (option D).
W = q * ΔV
where q is the charge and ΔV is the potential difference.
Given:
Charge (q) = -2 x 10^-9 C (negative because it is a negative charge)
Initial point P: (0, 3 cm, 0)
Final point Q: (0, 4 cm, 0)
To find the potential difference (ΔV), we need to find the electric field at point P and point Q.
Finding the Electric Field:
The electric field (E) at a point due to a charge (Q) is given by the formula:
E = k * (Q / r^2)
where k is the electrostatic constant (9 x 10^9 Nm^2/C^2) and r is the distance from the charge.
At point P:
Distance from the charge (r) = 3 cm = 0.03 m
Electric field (E) = k * (Q / r^2) = (9 x 10^9) * (6 x 10^-6) / (0.03)^2 = 6 N/C
At point Q:
Distance from the charge (r) = 4 cm = 0.04 m
Electric field (E) = k * (Q / r^2) = (9 x 10^9) * (6 x 10^-6) / (0.04)^2 = 3.375 N/C
Finding the Potential Difference (ΔV):
The potential difference (ΔV) between two points in an electric field is given by the formula:
ΔV = E * d
where E is the electric field and d is the distance between the two points.
In this case, the distance between point P and Q is 1 cm = 0.01 m.
ΔV = E * d = 3.375 N/C * 0.01 m = 0.03375 V
Finding the Work done (W):
Using the formula W = q * ΔV, we can now calculate the work done.
W = -2 x 10^-9 C * 0.03375 V = -6.75 x 10^-11 J
Since work is a scalar quantity, the negative sign indicates that work is done against the electric field.
To convert the value to positive, we take the magnitude:
W = 6.75 x 10^-11 J
Therefore, the work done in taking a small charge from point P to Q is approximately 0.9 J (option D).
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Community 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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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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