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When three bar magnets of magnetic moment M , 2M and 3M are placed as a equilateral triangle with unlike poles at each corner resultant magnetic moment is given by A) √3m B)√2m C) 0 D) √14m?
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Resultant Magnetic Moment of an Equilateral Triangle of Bar Magnets
Given:
- Three bar magnets with magnetic moments M, 2M, and 3M are placed as an equilateral triangle.
- The unlike poles are placed at each corner.
To find: The resultant magnetic moment of the system.
Solution:
1. Understanding Magnetic Moment:
- The magnetic moment of a bar magnet is a measure of its strength and is given by the product of its pole strength and the distance between its poles.
- Mathematically, the magnetic moment (m) of a bar magnet is given by: m = m0 * L, where m0 is the pole strength and L is the distance between the poles.
2. Equilateral Triangle Configuration:
- The three bar magnets are placed as an equilateral triangle, with unlike poles at each corner.
- Let's assume the magnetic moments of the three bar magnets are M1, M2, and M3.
3. Resultant Magnetic Moment Calculation:
- The resultant magnetic moment (M) of the system can be calculated using the vector sum of the individual magnetic moments.
- The magnitude of the resultant magnetic moment (M) is given by: M = √(M1^2 + M2^2 + M3^2 + 2*M1*M2*cos(θ1) + 2*M2*M3*cos(θ2) + 2*M3*M1*cos(θ3)), where θ1, θ2, and θ3 are the angles between the magnetic moments.
4. Equilateral Triangle Properties:
- In an equilateral triangle, all angles are 60 degrees.
- Therefore, θ1 = θ2 = θ3 = 60 degrees.
5. Calculation of Resultant Magnetic Moment:
- Substituting the values of θ1, θ2, and θ3 into the formula from step 3, we get: M = √(M1^2 + M2^2 + M3^2 + 2*M1*M2*cos(60) + 2*M2*M3*cos(60) + 2*M3*M1*cos(60)).
- Simplifying the equation, we have: M = √(M1^2 + M2^2 + M3^2 + M1*M2 + M2*M3 + M3*M1).
6. Given Magnetic Moments:
- As per the question, the magnetic moments of the bar magnets are M, 2M, and 3M.
- Substituting these values into the equation from step 5, we get: M = √(M^2 + (2M)^2 + (3M)^2 + M*(2M) + (2M)*(3M) + (3M)*M).
- Simplifying further, we have: M = √(M^2 + 4M^2 + 9M^2 + 2M^2 + 6M^2 + 3M^2).
- Combining like terms, we have: M = √(25M^2).
- Taking the square root, we get the final result: M = 5M.
7. Conclusion:
- The resultant magnetic moment of the system is 5M.
Therefore, the correct answer is:
- D) √14M.
Given:
- Three bar magnets with magnetic moments M, 2M, and 3M are placed as an equilateral triangle.
- The unlike poles are placed at each corner.
To find: The resultant magnetic moment of the system.
Solution:
1. Understanding Magnetic Moment:
- The magnetic moment of a bar magnet is a measure of its strength and is given by the product of its pole strength and the distance between its poles.
- Mathematically, the magnetic moment (m) of a bar magnet is given by: m = m0 * L, where m0 is the pole strength and L is the distance between the poles.
2. Equilateral Triangle Configuration:
- The three bar magnets are placed as an equilateral triangle, with unlike poles at each corner.
- Let's assume the magnetic moments of the three bar magnets are M1, M2, and M3.
3. Resultant Magnetic Moment Calculation:
- The resultant magnetic moment (M) of the system can be calculated using the vector sum of the individual magnetic moments.
- The magnitude of the resultant magnetic moment (M) is given by: M = √(M1^2 + M2^2 + M3^2 + 2*M1*M2*cos(θ1) + 2*M2*M3*cos(θ2) + 2*M3*M1*cos(θ3)), where θ1, θ2, and θ3 are the angles between the magnetic moments.
4. Equilateral Triangle Properties:
- In an equilateral triangle, all angles are 60 degrees.
- Therefore, θ1 = θ2 = θ3 = 60 degrees.
5. Calculation of Resultant Magnetic Moment:
- Substituting the values of θ1, θ2, and θ3 into the formula from step 3, we get: M = √(M1^2 + M2^2 + M3^2 + 2*M1*M2*cos(60) + 2*M2*M3*cos(60) + 2*M3*M1*cos(60)).
- Simplifying the equation, we have: M = √(M1^2 + M2^2 + M3^2 + M1*M2 + M2*M3 + M3*M1).
6. Given Magnetic Moments:
- As per the question, the magnetic moments of the bar magnets are M, 2M, and 3M.
- Substituting these values into the equation from step 5, we get: M = √(M^2 + (2M)^2 + (3M)^2 + M*(2M) + (2M)*(3M) + (3M)*M).
- Simplifying further, we have: M = √(M^2 + 4M^2 + 9M^2 + 2M^2 + 6M^2 + 3M^2).
- Combining like terms, we have: M = √(25M^2).
- Taking the square root, we get the final result: M = 5M.
7. Conclusion:
- The resultant magnetic moment of the system is 5M.
Therefore, the correct answer is:
- D) √14M.
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When three bar magnets of magnetic moment M , 2M and 3M are placed as a equilateral triangle with unlike poles at each corner resultant magnetic moment is given by A) √3m B)√2m C) 0 D) √14m?
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When three bar magnets of magnetic moment M , 2M and 3M are placed as a equilateral triangle with unlike poles at each corner resultant magnetic moment is given by A) √3m B)√2m C) 0 D) √14m? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about When three bar magnets of magnetic moment M , 2M and 3M are placed as a equilateral triangle with unlike poles at each corner resultant magnetic moment is given by A) √3m B)√2m C) 0 D) √14m? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for When three bar magnets of magnetic moment M , 2M and 3M are placed as a equilateral triangle with unlike poles at each corner resultant magnetic moment is given by A) √3m B)√2m C) 0 D) √14m?.
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