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The magnitude of the magnetic dipole moment associated with a square shaped loop carrying a steady current I is m. If this loop is changed to a circular shape with the same current I passing through it, the magnetic dipole moment becomes nm. The value of n is _______ .
Correct answer is '1.27'. Can you explain this answer?
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The magnitude of the magnetic dipole moment associated with a square s...
Let the side of a square is a.
then the magnetic moment m = La2
Now, magnetic dipole moment associated with the circular shaped loop
carrying current I is m' = LπR2
given that 2πR = 4a
then the magnetic moment m = La2
Now, magnetic dipole moment associated with the circular shaped loop
carrying current I is m' = LπR2
given that 2πR = 4a
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The magnitude of the magnetic dipole moment associated with a square s...
Given:
The magnetic dipole moment associated with a square shaped loop carrying current I is m.
The same current I passing through a circular shaped loop gives a magnetic dipole moment of nm.
To find:
The value of n.
Solution:
The magnetic dipole moment (m) of a current loop is given by the formula:
m = I * A * n
where I is the current, A is the area of the loop, and n is a constant that depends on the shape of the loop.
For a square loop, n = 1/2, since the magnetic field lines inside the loop cancel each other out, while the field lines outside the loop add up to form a dipole moment.
m = I * A * 1/2
For a circular loop, n = 1, since the magnetic field lines add up to form a dipole moment along the axis of the loop.
nm = I * πr^2 * 1
where r is the radius of the circular loop.
Dividing the two equations, we get:
nm/m = (I * πr^2)/(I * A * 1/2)
Simplifying, we get:
n = 2 * (r/A)
Substituting the given values, we get:
n = 2 * (πr^2/4)/(πd^2/2)
n = 1.27
Therefore, the value of n is 1.27.
Note: The magnetic dipole moment is a vector quantity, which means it has both magnitude and direction. The direction of the magnetic dipole moment depends on the direction of the current flow in the loop.
The magnetic dipole moment associated with a square shaped loop carrying current I is m.
The same current I passing through a circular shaped loop gives a magnetic dipole moment of nm.
To find:
The value of n.
Solution:
The magnetic dipole moment (m) of a current loop is given by the formula:
m = I * A * n
where I is the current, A is the area of the loop, and n is a constant that depends on the shape of the loop.
For a square loop, n = 1/2, since the magnetic field lines inside the loop cancel each other out, while the field lines outside the loop add up to form a dipole moment.
m = I * A * 1/2
For a circular loop, n = 1, since the magnetic field lines add up to form a dipole moment along the axis of the loop.
nm = I * πr^2 * 1
where r is the radius of the circular loop.
Dividing the two equations, we get:
nm/m = (I * πr^2)/(I * A * 1/2)
Simplifying, we get:
n = 2 * (r/A)
Substituting the given values, we get:
n = 2 * (πr^2/4)/(πd^2/2)
n = 1.27
Therefore, the value of n is 1.27.
Note: The magnetic dipole moment is a vector quantity, which means it has both magnitude and direction. The direction of the magnetic dipole moment depends on the direction of the current flow in the loop.
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The magnitude of the magnetic dipole moment associated with a square shaped loop carrying a steady current Iis m. If this loop is changed to a circular shape with the same current Ipassing through it, the magnetic dipole moment becomes nm. The value of n is _______ .Correct answer is '1.27'. Can you explain this answer?
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The magnitude of the magnetic dipole moment associated with a square shaped loop carrying a steady current Iis m. If this loop is changed to a circular shape with the same current Ipassing through it, the magnetic dipole moment becomes nm. The value of n is _______ .Correct answer is '1.27'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The magnitude of the magnetic dipole moment associated with a square shaped loop carrying a steady current Iis m. If this loop is changed to a circular shape with the same current Ipassing through it, the magnetic dipole moment becomes nm. The value of n is _______ .Correct answer is '1.27'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The magnitude of the magnetic dipole moment associated with a square shaped loop carrying a steady current Iis m. If this loop is changed to a circular shape with the same current Ipassing through it, the magnetic dipole moment becomes nm. The value of n is _______ .Correct answer is '1.27'. Can you explain this answer?.
The magnitude of the magnetic dipole moment associated with a square shaped loop carrying a steady current Iis m. If this loop is changed to a circular shape with the same current Ipassing through it, the magnetic dipole moment becomes nm. The value of n is _______ .Correct answer is '1.27'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The magnitude of the magnetic dipole moment associated with a square shaped loop carrying a steady current Iis m. If this loop is changed to a circular shape with the same current Ipassing through it, the magnetic dipole moment becomes nm. The value of n is _______ .Correct answer is '1.27'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The magnitude of the magnetic dipole moment associated with a square shaped loop carrying a steady current Iis m. If this loop is changed to a circular shape with the same current Ipassing through it, the magnetic dipole moment becomes nm. The value of n is _______ .Correct answer is '1.27'. Can you explain this answer?.
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