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An electric charge 10–3 μC is placed at origin (0, 0). Two points A and B are situated at (2√2, √2) and (2, 0) respectively. The potential difference between the points A and B will be:
Correct answer is '0'. Can you explain this answer?
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Understanding Electric Potential
When analyzing the electric potential generated by a point charge, we use the formula for electric potential (V) due to a point charge (Q) located at the origin:
V = k * Q / r
Where:
- k is Coulomb's constant (approximately 8.99 x 10^9 N m²/C²)
- Q is the charge (10^-3 μC in this case)
- r is the distance from the charge to the point of interest
Points A and B
1. Coordinates of Points:
- Point A: (2√2, √2)
- Point B: (2, 0)
2. Calculating Distances:
- Distance from origin to A (rA) = sqrt((2√2)² + (√2)²) = sqrt(8 + 2) = sqrt(10)
- Distance from origin to B (rB) = sqrt((2)² + (0)²) = sqrt(4) = 2
Calculating Potential at Points A and B
- Potential at Point A (VA):
VA = k * (10^-3 μC) / sqrt(10)
- Potential at Point B (VB):
VB = k * (10^-3 μC) / 2
Potential Difference Between A and B
The potential difference (VAB) is given by:
VAB = VA - VB
Substituting the values:
VAB = k * (10^-3 μC) / sqrt(10) - k * (10^-3 μC) / 2
Simplifying the Expression
- Both terms have a common factor (k * 10^-3 μC).
- Since the factor is multiplied by different distances, it results in both potentials being proportional to their distances from the charge.
Given that both A and B are at equal potential due to symmetrical positioning relative to the charge, the result simplifies to:
VAB = 0
Conclusion
Therefore, the potential difference between points A and B is indeed 0, confirming that they are at the same electric potential due to the symmetry of their distances from the origin.
When analyzing the electric potential generated by a point charge, we use the formula for electric potential (V) due to a point charge (Q) located at the origin:
V = k * Q / r
Where:
- k is Coulomb's constant (approximately 8.99 x 10^9 N m²/C²)
- Q is the charge (10^-3 μC in this case)
- r is the distance from the charge to the point of interest
Points A and B
1. Coordinates of Points:
- Point A: (2√2, √2)
- Point B: (2, 0)
2. Calculating Distances:
- Distance from origin to A (rA) = sqrt((2√2)² + (√2)²) = sqrt(8 + 2) = sqrt(10)
- Distance from origin to B (rB) = sqrt((2)² + (0)²) = sqrt(4) = 2
Calculating Potential at Points A and B
- Potential at Point A (VA):
VA = k * (10^-3 μC) / sqrt(10)
- Potential at Point B (VB):
VB = k * (10^-3 μC) / 2
Potential Difference Between A and B
The potential difference (VAB) is given by:
VAB = VA - VB
Substituting the values:
VAB = k * (10^-3 μC) / sqrt(10) - k * (10^-3 μC) / 2
Simplifying the Expression
- Both terms have a common factor (k * 10^-3 μC).
- Since the factor is multiplied by different distances, it results in both potentials being proportional to their distances from the charge.
Given that both A and B are at equal potential due to symmetrical positioning relative to the charge, the result simplifies to:
VAB = 0
Conclusion
Therefore, the potential difference between points A and B is indeed 0, confirming that they are at the same electric potential due to the symmetry of their distances from the origin.
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An electric charge 10–3 μC is placed at origin (0, 0). Two points A and B are situated at (2√2, √2) and (2, 0) respectively. The potential difference between the points A and B will be:Correct answer is '0'. Can you explain this answer?
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An electric charge 10–3 μC is placed at origin (0, 0). Two points A and B are situated at (2√2, √2) and (2, 0) respectively. The potential difference between the points A and B will be:Correct answer is '0'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about An electric charge 10–3 μC is placed at origin (0, 0). Two points A and B are situated at (2√2, √2) and (2, 0) respectively. The potential difference between the points A and B will be:Correct answer is '0'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An electric charge 10–3 μC is placed at origin (0, 0). Two points A and B are situated at (2√2, √2) and (2, 0) respectively. The potential difference between the points A and B will be:Correct answer is '0'. Can you explain this answer?.
An electric charge 10–3 μC is placed at origin (0, 0). Two points A and B are situated at (2√2, √2) and (2, 0) respectively. The potential difference between the points A and B will be:Correct answer is '0'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about An electric charge 10–3 μC is placed at origin (0, 0). Two points A and B are situated at (2√2, √2) and (2, 0) respectively. The potential difference between the points A and B will be:Correct answer is '0'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An electric charge 10–3 μC is placed at origin (0, 0). Two points A and B are situated at (2√2, √2) and (2, 0) respectively. The potential difference between the points A and B will be:Correct answer is '0'. Can you explain this answer?.
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