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If charge is uniformly distributed in xy plane with chrge density +σ in the first quadrant and -σ in in the remaining three quadrants ,then work done by electric field in moving a point charge from (0,0,d) to (0,0,2d) ,is. a) σqd/4ε. b) σqd/ε c)-σqd/2ε. d) none of these
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If charge is uniformly distributed in xy plane with chrge density +σ ...
Calculating the Electric Field
To calculate the work done by the electric field, we need to first calculate the electric field at every point along the path of the point charge. We can do this by using the principle of superposition, which states that the electric field at any given point is equal to the vector sum of the electric fields created by each individual charge in the system.
Breaking the Path into Segments
To simplify the calculation, we can break the path into segments and calculate the electric field at the midpoint of each segment. We can then use the equation for the work done by a constant electric field to calculate the work done along each segment.
Calculating the Work Done
Finally, we can add up the work done along each segment to find the total work done by the electric field in moving the point charge from (0,0,d) to (0,0,2d).
Answer
The correct answer is c) -σqd/2ε.
Explanation
When we calculate the electric field at a point in the first quadrant, we find that it points in the negative z direction. This means that it will do negative work on the point charge as it moves from (0,0,d) to (0,0,2d).
On the other hand, when we calculate the electric field at a point in the other three quadrants, we find that it points in the positive z direction. This means that it will do positive work on the point charge as it moves from (0,0,d) to (0,0,2d).
Since there is symmetry in the problem, we know that the magnitude of the electric field is the same at corresponding points in the first and fourth quadrants, and in the second and third quadrants. This allows us to simplify the calculation.
Using the principle of superposition, we can calculate the electric field at the midpoint of each segment of the path. We find that the magnitude of the electric field is given by:
E = σd/2ε
where σ is the charge density, d is the distance from the origin to the midpoint of the segment, and ε is the permittivity of free space.
Using the equation for the work done by a constant electric field, we can calculate the work done along each segment:
W = -qEd/2
where q is the charge of the point charge, and the negative sign indicates that the electric field does negative work on the point charge as it moves in the negative z direction.
Adding up the work done along each segment, we find that the total work done by the electric field is:
W = -σqd/2ε
Therefore, the correct answer is c) -σqd/2ε.
To calculate the work done by the electric field, we need to first calculate the electric field at every point along the path of the point charge. We can do this by using the principle of superposition, which states that the electric field at any given point is equal to the vector sum of the electric fields created by each individual charge in the system.
Breaking the Path into Segments
To simplify the calculation, we can break the path into segments and calculate the electric field at the midpoint of each segment. We can then use the equation for the work done by a constant electric field to calculate the work done along each segment.
Calculating the Work Done
Finally, we can add up the work done along each segment to find the total work done by the electric field in moving the point charge from (0,0,d) to (0,0,2d).
Answer
The correct answer is c) -σqd/2ε.
Explanation
When we calculate the electric field at a point in the first quadrant, we find that it points in the negative z direction. This means that it will do negative work on the point charge as it moves from (0,0,d) to (0,0,2d).
On the other hand, when we calculate the electric field at a point in the other three quadrants, we find that it points in the positive z direction. This means that it will do positive work on the point charge as it moves from (0,0,d) to (0,0,2d).
Since there is symmetry in the problem, we know that the magnitude of the electric field is the same at corresponding points in the first and fourth quadrants, and in the second and third quadrants. This allows us to simplify the calculation.
Using the principle of superposition, we can calculate the electric field at the midpoint of each segment of the path. We find that the magnitude of the electric field is given by:
E = σd/2ε
where σ is the charge density, d is the distance from the origin to the midpoint of the segment, and ε is the permittivity of free space.
Using the equation for the work done by a constant electric field, we can calculate the work done along each segment:
W = -qEd/2
where q is the charge of the point charge, and the negative sign indicates that the electric field does negative work on the point charge as it moves in the negative z direction.
Adding up the work done along each segment, we find that the total work done by the electric field is:
W = -σqd/2ε
Therefore, the correct answer is c) -σqd/2ε.
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If charge is uniformly distributed in xy plane with chrge density +σ ...
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If charge is uniformly distributed in xy plane with chrge density +σ in the first quadrant and -σ in in the remaining three quadrants ,then work done by electric field in moving a point charge from (0,0,d) to (0,0,2d) ,is. a) σqd/4ε. b) σqd/ε c)-σqd/2ε. d) none of these
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If charge is uniformly distributed in xy plane with chrge density +σ in the first quadrant and -σ in in the remaining three quadrants ,then work done by electric field in moving a point charge from (0,0,d) to (0,0,2d) ,is. a) σqd/4ε. b) σqd/ε c)-σqd/2ε. d) none of these for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about If charge is uniformly distributed in xy plane with chrge density +σ in the first quadrant and -σ in in the remaining three quadrants ,then work done by electric field in moving a point charge from (0,0,d) to (0,0,2d) ,is. a) σqd/4ε. b) σqd/ε c)-σqd/2ε. d) none of these covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If charge is uniformly distributed in xy plane with chrge density +σ in the first quadrant and -σ in in the remaining three quadrants ,then work done by electric field in moving a point charge from (0,0,d) to (0,0,2d) ,is. a) σqd/4ε. b) σqd/ε c)-σqd/2ε. d) none of these.
If charge is uniformly distributed in xy plane with chrge density +σ in the first quadrant and -σ in in the remaining three quadrants ,then work done by electric field in moving a point charge from (0,0,d) to (0,0,2d) ,is. a) σqd/4ε. b) σqd/ε c)-σqd/2ε. d) none of these for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about If charge is uniformly distributed in xy plane with chrge density +σ in the first quadrant and -σ in in the remaining three quadrants ,then work done by electric field in moving a point charge from (0,0,d) to (0,0,2d) ,is. a) σqd/4ε. b) σqd/ε c)-σqd/2ε. d) none of these covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If charge is uniformly distributed in xy plane with chrge density +σ in the first quadrant and -σ in in the remaining three quadrants ,then work done by electric field in moving a point charge from (0,0,d) to (0,0,2d) ,is. a) σqd/4ε. b) σqd/ε c)-σqd/2ε. d) none of these.
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