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Two wires of same length are shaped into a square and a circle. If they carry same current, ratio of the magnetic moment is
- a)2 : π
- b)4 : π
- c)π : 2
- d)π : 4
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Two wires of same length are shaped into a square and a circle. If the...
Let length of each wire is L
For square length of each side L/4
For square length of each side L/4
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Two wires of same length are shaped into a square and a circle. If the...
The magnetic moment of a current-carrying wire is given by the formula:
Magnetic moment (μ) = current (I) x area (A) x number of turns (N)
For the wire shaped into a square, the area is equal to the side length squared:
A_square = side_length^2
For the wire shaped into a circle, the area is given by the formula:
A_circle = π x radius^2
Since both wires have the same length, the perimeter of the square is equal to the circumference of the circle:
4 x side_length = 2π x radius
Simplifying the equation, we get:
side_length = (π/2) x radius
Substituting this into the area formula for the square, we get:
A_square = ((π/2) x radius)^2
Simplifying further:
A_square = (π^2/4) x radius^2
Now we can compare the areas of the square and the circle:
A_square / A_circle = ((π^2/4) x radius^2) / (π x radius^2)
The radius^2 term cancels out, leaving:
A_square / A_circle = π/4
Since the current is the same for both wires, the ratio of their magnetic moments is equal to the ratio of their areas:
M_square / M_circle = A_square / A_circle = π/4
Therefore, the ratio of the magnetic moments is 1 : (π/4), which is approximately 1 : 0.785.
Magnetic moment (μ) = current (I) x area (A) x number of turns (N)
For the wire shaped into a square, the area is equal to the side length squared:
A_square = side_length^2
For the wire shaped into a circle, the area is given by the formula:
A_circle = π x radius^2
Since both wires have the same length, the perimeter of the square is equal to the circumference of the circle:
4 x side_length = 2π x radius
Simplifying the equation, we get:
side_length = (π/2) x radius
Substituting this into the area formula for the square, we get:
A_square = ((π/2) x radius)^2
Simplifying further:
A_square = (π^2/4) x radius^2
Now we can compare the areas of the square and the circle:
A_square / A_circle = ((π^2/4) x radius^2) / (π x radius^2)
The radius^2 term cancels out, leaving:
A_square / A_circle = π/4
Since the current is the same for both wires, the ratio of their magnetic moments is equal to the ratio of their areas:
M_square / M_circle = A_square / A_circle = π/4
Therefore, the ratio of the magnetic moments is 1 : (π/4), which is approximately 1 : 0.785.
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Two wires of same length are shaped into a square and a circle. If they carry same current, ratio of the magnetic moment isa)2 :πb)4 :πc)π : 2d)π : 4Correct answer is option 'D'. Can you explain this answer? for Physics 2025 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Two wires of same length are shaped into a square and a circle. If they carry same current, ratio of the magnetic moment isa)2 :πb)4 :πc)π : 2d)π : 4Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Physics 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two wires of same length are shaped into a square and a circle. If they carry same current, ratio of the magnetic moment isa)2 :πb)4 :πc)π : 2d)π : 4Correct answer is option 'D'. Can you explain this answer?.
Two wires of same length are shaped into a square and a circle. If they carry same current, ratio of the magnetic moment isa)2 :πb)4 :πc)π : 2d)π : 4Correct answer is option 'D'. Can you explain this answer? for Physics 2025 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Two wires of same length are shaped into a square and a circle. If they carry same current, ratio of the magnetic moment isa)2 :πb)4 :πc)π : 2d)π : 4Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Physics 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two wires of same length are shaped into a square and a circle. If they carry same current, ratio of the magnetic moment isa)2 :πb)4 :πc)π : 2d)π : 4Correct answer is option 'D'. Can you explain this answer?.
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