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A magnetic needle having moment of inertia 10^-6 kg m^2 performs 10 oscillations of small amplitude in 6.28 seconds in uniform magnetic field of 25 gauss, the magnetic movement of the needle is.?
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A magnetic needle having moment of inertia 10^-6 kg m^2 performs 10 os...
Introduction
To determine the magnetic moment of a magnetic needle oscillating in a magnetic field, we can use the relationship between the oscillation frequency, moment of inertia, and the magnetic field strength.
Given Data
- Moment of Inertia (I) = \(10^{-6}\) kg m²
- Number of oscillations (n) = 10
- Time for oscillations (T) = 6.28 seconds
- Magnetic field (B) = 25 gauss = \(25 \times 10^{-4}\) T
Calculation of Frequency
- The time period (T) for one oscillation is given by:
- The angular frequency (\(\omega\)) is given by:
Relationship Between Frequency and Magnetic Moment
- The formula for angular frequency \(\omega\) is:
- Rearranging gives:
Substituting Values
- Now, substituting the known values:
Conclusion
The magnetic moment of the needle is \(0.04 \text{ Am}^2\). This calculation demonstrates how oscillation properties relate to magnetic characteristics in a uniform magnetic field.
To determine the magnetic moment of a magnetic needle oscillating in a magnetic field, we can use the relationship between the oscillation frequency, moment of inertia, and the magnetic field strength.
Given Data
- Moment of Inertia (I) = \(10^{-6}\) kg m²
- Number of oscillations (n) = 10
- Time for oscillations (T) = 6.28 seconds
- Magnetic field (B) = 25 gauss = \(25 \times 10^{-4}\) T
Calculation of Frequency
- The time period (T) for one oscillation is given by:
- T = Total Time / Number of Oscillations
- T = 6.28 seconds / 10 = 0.628 seconds
- The angular frequency (\(\omega\)) is given by:
- \(\omega = \frac{2\pi}{T} = \frac{2\pi}{0.628} \approx 10\) rad/s
Relationship Between Frequency and Magnetic Moment
- The formula for angular frequency \(\omega\) is:
- \(\omega = \sqrt{\frac{mB}{I}}\) where m is the magnetic moment.
- Rearranging gives:
- m = \frac{\omega^2 \cdot I}{B}
Substituting Values
- Now, substituting the known values:
- m = \frac{(10)^2 \cdot (10^{-6})}{25 \times 10^{-4}}
- m = \frac{100 \times 10^{-6}}{25 \times 10^{-4}} = \frac{100 \times 10^{-6}}{0.0025} = 0.04 \text{ Am}^2
Conclusion
The magnetic moment of the needle is \(0.04 \text{ Am}^2\). This calculation demonstrates how oscillation properties relate to magnetic characteristics in a uniform magnetic field.
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A magnetic needle having moment of inertia 10^-6 kg m^2 performs 10 oscillations of small amplitude in 6.28 seconds in uniform magnetic field of 25 gauss, the magnetic movement of the needle is.?
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A magnetic needle having moment of inertia 10^-6 kg m^2 performs 10 oscillations of small amplitude in 6.28 seconds in uniform magnetic field of 25 gauss, the magnetic movement of the needle is.? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A magnetic needle having moment of inertia 10^-6 kg m^2 performs 10 oscillations of small amplitude in 6.28 seconds in uniform magnetic field of 25 gauss, the magnetic movement of the needle is.? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A magnetic needle having moment of inertia 10^-6 kg m^2 performs 10 oscillations of small amplitude in 6.28 seconds in uniform magnetic field of 25 gauss, the magnetic movement of the needle is.?.
A magnetic needle having moment of inertia 10^-6 kg m^2 performs 10 oscillations of small amplitude in 6.28 seconds in uniform magnetic field of 25 gauss, the magnetic movement of the needle is.? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A magnetic needle having moment of inertia 10^-6 kg m^2 performs 10 oscillations of small amplitude in 6.28 seconds in uniform magnetic field of 25 gauss, the magnetic movement of the needle is.? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A magnetic needle having moment of inertia 10^-6 kg m^2 performs 10 oscillations of small amplitude in 6.28 seconds in uniform magnetic field of 25 gauss, the magnetic movement of the needle is.?.
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