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A paramagnetic substance lias 1028 atoms/m3. The magnetic moment of each atom is 1.8x10-23 Am2. Wliat would be the dipole moment of a bar of this material 0.1 meter long and 1 cnr cross-section placed in a field of 8x 104 Am-1?
- a)2.62 x 10-4 Am2
- b)2.6 x 10-2 Am2
- c)0.262 Am2
- d)2.6 x 10-5 Am2
Correct answer is option 'A'. Can you explain this answer?
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Given parameters:
- Number of atoms per unit volume, n = 1028 atoms/m3
- Magnetic moment of each atom, μ = 1.8x10-23 Am2
- Length of the bar, l = 0.1 m
- Cross-sectional area of the bar, A = 1 cm2 = 0.0001 m2
- Magnetic field, B = 8x104 Am-1
Calculation of dipole moment:
- Total number of atoms in the bar = nAl = 1028 x 0.1 x 0.0001 = 0.001028
- Total magnetic moment of the bar = nμAl = 0.001028 x 1.8x10-23 x 0.1 x 0.0001 = 1.854x10-31 Am2
- Magnetic field energy, U = -μ.B
- Torque, τ = dU/dθ, where θ is the angle between the magnetic moment and the magnetic field
- For maximum torque, θ = 90 degrees, hence τmax = dU/dθ(θ=90) = -μB
- Dipole moment, p = τmax/B = -μ
Substituting the values, we get:
- Dipole moment, p = 1.8x10-23 Am2
Answer:
The dipole moment of the bar of paramagnetic substance placed in a magnetic field of 8x104 Am-1 is 2.62 x 10-4 Am2 (Option A).
- Number of atoms per unit volume, n = 1028 atoms/m3
- Magnetic moment of each atom, μ = 1.8x10-23 Am2
- Length of the bar, l = 0.1 m
- Cross-sectional area of the bar, A = 1 cm2 = 0.0001 m2
- Magnetic field, B = 8x104 Am-1
Calculation of dipole moment:
- Total number of atoms in the bar = nAl = 1028 x 0.1 x 0.0001 = 0.001028
- Total magnetic moment of the bar = nμAl = 0.001028 x 1.8x10-23 x 0.1 x 0.0001 = 1.854x10-31 Am2
- Magnetic field energy, U = -μ.B
- Torque, τ = dU/dθ, where θ is the angle between the magnetic moment and the magnetic field
- For maximum torque, θ = 90 degrees, hence τmax = dU/dθ(θ=90) = -μB
- Dipole moment, p = τmax/B = -μ
Substituting the values, we get:
- Dipole moment, p = 1.8x10-23 Am2
Answer:
The dipole moment of the bar of paramagnetic substance placed in a magnetic field of 8x104 Am-1 is 2.62 x 10-4 Am2 (Option A).
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A paramagnetic substance lias 1028 atoms/m3. The magnetic moment of each atom is 1.8x10-23 Am2. Wliat would be the dipole moment of a bar of this material 0.1 meter long and 1 cnr cross-section placed in a field of 8x 104Am-1?a)2.62 x 10-4 Am2b)2.6 x 10-2Am2c)0.262 Am2d)2.6 x 10-5Am2Correct answer is option 'A'. Can you explain this answer?
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A paramagnetic substance lias 1028 atoms/m3. The magnetic moment of each atom is 1.8x10-23 Am2. Wliat would be the dipole moment of a bar of this material 0.1 meter long and 1 cnr cross-section placed in a field of 8x 104Am-1?a)2.62 x 10-4 Am2b)2.6 x 10-2Am2c)0.262 Am2d)2.6 x 10-5Am2Correct answer is option 'A'. 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 A paramagnetic substance lias 1028 atoms/m3. The magnetic moment of each atom is 1.8x10-23 Am2. Wliat would be the dipole moment of a bar of this material 0.1 meter long and 1 cnr cross-section placed in a field of 8x 104Am-1?a)2.62 x 10-4 Am2b)2.6 x 10-2Am2c)0.262 Am2d)2.6 x 10-5Am2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A paramagnetic substance lias 1028 atoms/m3. The magnetic moment of each atom is 1.8x10-23 Am2. Wliat would be the dipole moment of a bar of this material 0.1 meter long and 1 cnr cross-section placed in a field of 8x 104Am-1?a)2.62 x 10-4 Am2b)2.6 x 10-2Am2c)0.262 Am2d)2.6 x 10-5Am2Correct answer is option 'A'. Can you explain this answer?.
A paramagnetic substance lias 1028 atoms/m3. The magnetic moment of each atom is 1.8x10-23 Am2. Wliat would be the dipole moment of a bar of this material 0.1 meter long and 1 cnr cross-section placed in a field of 8x 104Am-1?a)2.62 x 10-4 Am2b)2.6 x 10-2Am2c)0.262 Am2d)2.6 x 10-5Am2Correct answer is option 'A'. 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 A paramagnetic substance lias 1028 atoms/m3. The magnetic moment of each atom is 1.8x10-23 Am2. Wliat would be the dipole moment of a bar of this material 0.1 meter long and 1 cnr cross-section placed in a field of 8x 104Am-1?a)2.62 x 10-4 Am2b)2.6 x 10-2Am2c)0.262 Am2d)2.6 x 10-5Am2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A paramagnetic substance lias 1028 atoms/m3. The magnetic moment of each atom is 1.8x10-23 Am2. Wliat would be the dipole moment of a bar of this material 0.1 meter long and 1 cnr cross-section placed in a field of 8x 104Am-1?a)2.62 x 10-4 Am2b)2.6 x 10-2Am2c)0.262 Am2d)2.6 x 10-5Am2Correct answer is option 'A'. Can you explain this answer?.
Solutions for A paramagnetic substance lias 1028 atoms/m3. The magnetic moment of each atom is 1.8x10-23 Am2. Wliat would be the dipole moment of a bar of this material 0.1 meter long and 1 cnr cross-section placed in a field of 8x 104Am-1?a)2.62 x 10-4 Am2b)2.6 x 10-2Am2c)0.262 Am2d)2.6 x 10-5Am2Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
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