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A circular coil and a square coil is prepared from two identical metal wires and a current is passed through The ratio of magnetic dipole moment associated with circular coil to that of square coil is
- a)2/π
- b)π/2
- c)π
- d)4/π
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A circular coil and a square coil is prepared from two identical meta...
Let l be the length of metal wire. When wire is bent into a circular coil of radius r, then r = l/2π
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∴ Area, 
∴ Magnetic dipole moment associated with circular coil,
μc = il2/4π …(i)
When metal wire is bent into a square coil then side of square a = l/4
∴ Area, A = a2 = l2/16
∴ Magnetic dipole moment associated with square coil, μc = iA = i(l2/16)
∴ 
Hnce, the ratio of magnetic dipole moment of circular coil and square coil is 4 : π.
Most Upvoted Answer
A circular coil and a square coil is prepared from two identical meta...
Solution:
Given, two identical metal wires are used to prepare circular and square coils, and a current is passed through them.
Let N be the number of turns in each coil, A be the area of each coil, and I be the current passing through each coil.
The magnetic dipole moment (M) associated with a coil is given by the product of the current passing through the coil, the area of the coil, and the number of turns in the coil.
M = NIA
For the circular coil, the area is given by the formula:
A = πr², where r is the radius of the coil.
For the square coil, the area is given by the formula:
A = a², where a is the length of one side of the square.
Since the two coils are made from identical wires, the current passing through each coil is the same (I).
Therefore, the ratio of magnetic dipole moment associated with circular coil to that of square coil is given by:
M(circular)/M(square) = (NIA(circular))/(NIA(square))
= (πr²)(I)/(a²)(I)
= πr²/a²
Now, it is given that the two coils are identical, which means that the radius of the circular coil is equal to the length of one side of the square coil.
Therefore, r = a/√2
Substituting this value in the above equation, we get:
M(circular)/M(square) = π(a/√2)²/a²
= π/2
Hence, the correct option is D.
Given, two identical metal wires are used to prepare circular and square coils, and a current is passed through them.
Let N be the number of turns in each coil, A be the area of each coil, and I be the current passing through each coil.
The magnetic dipole moment (M) associated with a coil is given by the product of the current passing through the coil, the area of the coil, and the number of turns in the coil.
M = NIA
For the circular coil, the area is given by the formula:
A = πr², where r is the radius of the coil.
For the square coil, the area is given by the formula:
A = a², where a is the length of one side of the square.
Since the two coils are made from identical wires, the current passing through each coil is the same (I).
Therefore, the ratio of magnetic dipole moment associated with circular coil to that of square coil is given by:
M(circular)/M(square) = (NIA(circular))/(NIA(square))
= (πr²)(I)/(a²)(I)
= πr²/a²
Now, it is given that the two coils are identical, which means that the radius of the circular coil is equal to the length of one side of the square coil.
Therefore, r = a/√2
Substituting this value in the above equation, we get:
M(circular)/M(square) = π(a/√2)²/a²
= π/2
Hence, the correct option is D.
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A circular coil and a square coil is prepared from two identical metal wires and a current is passed through The ratio of magnetic dipole moment associated with circular coil to that of square coil isa)2/πb)π/2c)πd)4/πCorrect answer is option 'D'. Can you explain this answer?
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