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Two magnets are placed one above the other with like poles together.The time period of this combination is 10 seconds. Now they are placed one above the other with unlike poles together. The time period of this combination in the same fields is 20 seconds. The ratio of the magnetic moment is -?
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Magnetic Moment and Time Period of Magnetic Combination
In this scenario, we have two magnets placed one above the other. Initially, the like poles are together, and later the unlike poles are together. We need to determine the ratio of their magnetic moments based on the different time periods observed for each combination.
1. Like Poles Together
When the like poles of two magnets are placed together, they repel each other. This repulsion creates a torque on the system, causing it to oscillate. The time period of this oscillation can be calculated using the formula:
T1 = 2π√(I / B)
where T1 is the time period, I is the moment of inertia of the system, and B is the magnetic field strength.
Given that the time period of this combination is 10 seconds, we can express the equation as:
10 = 2π√(I / B) ----(1)
2. Unlike Poles Together
When the unlike poles of two magnets are placed together, they attract each other. This attraction also creates a torque on the system, causing it to oscillate. The time period of this oscillation can be calculated using the same formula as before:
T2 = 2π√(I / B)
Given that the time period of this combination is 20 seconds, we can express the equation as:
20 = 2π√(I / B) ----(2)
Calculating the Ratio of Magnetic Moments
To determine the ratio of the magnetic moments, we can divide equation (2) by equation (1):
T2 / T1 = (2π√(I / B)) / (2π√(I / B))
Simplifying the equation, we get:
T2 / T1 = 20 / 10
T2 / T1 = 2
Therefore, the ratio of the time periods is 2. Since the time period is inversely proportional to the square root of the magnetic moment, the ratio of the magnetic moments can be calculated as the square of the ratio of time periods:
(M2 / M1)^2 = (T1 / T2)^2
Substituting the values, we have:
(M2 / M1)^2 = (1 / 2)^2
(M2 / M1)^2 = 1 / 4
Taking the square root of both sides, we get:
M2 / M1 = 1 / 2
Therefore, the ratio of the magnetic moments is 1:2, or 1/2, when the magnets are placed one above the other with unlike poles together.
This ratio indicates that the magnet with the unlike pole combination has half the magnetic moment of the magnet with the like pole combination.
In this scenario, we have two magnets placed one above the other. Initially, the like poles are together, and later the unlike poles are together. We need to determine the ratio of their magnetic moments based on the different time periods observed for each combination.
1. Like Poles Together
When the like poles of two magnets are placed together, they repel each other. This repulsion creates a torque on the system, causing it to oscillate. The time period of this oscillation can be calculated using the formula:
T1 = 2π√(I / B)
where T1 is the time period, I is the moment of inertia of the system, and B is the magnetic field strength.
Given that the time period of this combination is 10 seconds, we can express the equation as:
10 = 2π√(I / B) ----(1)
2. Unlike Poles Together
When the unlike poles of two magnets are placed together, they attract each other. This attraction also creates a torque on the system, causing it to oscillate. The time period of this oscillation can be calculated using the same formula as before:
T2 = 2π√(I / B)
Given that the time period of this combination is 20 seconds, we can express the equation as:
20 = 2π√(I / B) ----(2)
Calculating the Ratio of Magnetic Moments
To determine the ratio of the magnetic moments, we can divide equation (2) by equation (1):
T2 / T1 = (2π√(I / B)) / (2π√(I / B))
Simplifying the equation, we get:
T2 / T1 = 20 / 10
T2 / T1 = 2
Therefore, the ratio of the time periods is 2. Since the time period is inversely proportional to the square root of the magnetic moment, the ratio of the magnetic moments can be calculated as the square of the ratio of time periods:
(M2 / M1)^2 = (T1 / T2)^2
Substituting the values, we have:
(M2 / M1)^2 = (1 / 2)^2
(M2 / M1)^2 = 1 / 4
Taking the square root of both sides, we get:
M2 / M1 = 1 / 2
Therefore, the ratio of the magnetic moments is 1:2, or 1/2, when the magnets are placed one above the other with unlike poles together.
This ratio indicates that the magnet with the unlike pole combination has half the magnetic moment of the magnet with the like pole combination.
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Two magnets are placed one above the other with like poles together.The time period of this combination is 10 seconds. Now they are placed one above the other with unlike poles together. The time period of this combination in the same fields is 20 seconds. The ratio of the magnetic moment is -?
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Two magnets are placed one above the other with like poles together.The time period of this combination is 10 seconds. Now they are placed one above the other with unlike poles together. The time period of this combination in the same fields is 20 seconds. The ratio of the magnetic moment is -? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two magnets are placed one above the other with like poles together.The time period of this combination is 10 seconds. Now they are placed one above the other with unlike poles together. The time period of this combination in the same fields is 20 seconds. The ratio of the magnetic moment is -? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two magnets are placed one above the other with like poles together.The time period of this combination is 10 seconds. Now they are placed one above the other with unlike poles together. The time period of this combination in the same fields is 20 seconds. The ratio of the magnetic moment is -?.
Two magnets are placed one above the other with like poles together.The time period of this combination is 10 seconds. Now they are placed one above the other with unlike poles together. The time period of this combination in the same fields is 20 seconds. The ratio of the magnetic moment is -? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two magnets are placed one above the other with like poles together.The time period of this combination is 10 seconds. Now they are placed one above the other with unlike poles together. The time period of this combination in the same fields is 20 seconds. The ratio of the magnetic moment is -? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two magnets are placed one above the other with like poles together.The time period of this combination is 10 seconds. Now they are placed one above the other with unlike poles together. The time period of this combination in the same fields is 20 seconds. The ratio of the magnetic moment is -?.
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