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A bar magnet having a magnetic moment of 2×104JT−1 is free to rotate in a horizontal plane. A horizontal magnetic field B = 6×10−4T exists in the space. The work done in taking the magnet slowly from a direction parallel to the field to a direction 60° from the field is
- a)12 J
- b)6 J
- c)2 J
- d)0.6 J
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A bar magnet having a magnetic moment of 2×104JT−1 is free to rotate ...
Here,M = 2 × 104JT−1
B = 6 × 10−4T,θ1 = 0°,θ2 = 60°
W = MB(cosθ1 − cosθ2) = MB(1 − cos60°)
= 6 J
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A bar magnet having a magnetic moment of 2×104JT−1 is free to rotate ...
To find the work done in taking the magnet from a direction parallel to the magnetic field to a direction 60° from the field, we can use the equation:
W = -ΔU
Where W is the work done and ΔU is the change in potential energy.
The potential energy of a magnetic dipole in a magnetic field is given by the equation:
U = -m • B
Where U is the potential energy, m is the magnetic moment, and B is the magnetic field.
Let's calculate the potential energy at each direction and then find the change in potential energy.
1. Potential energy when the magnet is parallel to the field:
At this position, the angle between the magnetic moment and the magnetic field is 0°.
U1 = -m • B • cos(0°)
U1 = -m • B
2. Potential energy when the magnet is at 60° from the field:
At this position, the angle between the magnetic moment and the magnetic field is 60°.
U2 = -m • B • cos(60°)
U2 = -m • B • 0.5
U2 = -0.5 • U1
Now, let's calculate the change in potential energy:
ΔU = U2 - U1
ΔU = -0.5 • U1 - (-U1)
ΔU = -0.5 • U1 + U1
ΔU = 0.5 • U1
Finally, we can calculate the work done:
W = -ΔU
W = -0.5 • U1
Given that the magnetic moment of the bar magnet is 2×10^4 J T^-1 and the magnetic field is 6×10^-4 T, we can substitute these values into the equation:
W = -0.5 • (2×10^4 J T^-1) • (6×10^-4 T)
W = -0.5 • (2×10^4) • (6×10^-4) J
W = -6 J
Since work is a scalar quantity, the negative sign indicates that work is done by an external agent to change the orientation of the magnet.
Therefore, the correct answer is option B: 6 J.
W = -ΔU
Where W is the work done and ΔU is the change in potential energy.
The potential energy of a magnetic dipole in a magnetic field is given by the equation:
U = -m • B
Where U is the potential energy, m is the magnetic moment, and B is the magnetic field.
Let's calculate the potential energy at each direction and then find the change in potential energy.
1. Potential energy when the magnet is parallel to the field:
At this position, the angle between the magnetic moment and the magnetic field is 0°.
U1 = -m • B • cos(0°)
U1 = -m • B
2. Potential energy when the magnet is at 60° from the field:
At this position, the angle between the magnetic moment and the magnetic field is 60°.
U2 = -m • B • cos(60°)
U2 = -m • B • 0.5
U2 = -0.5 • U1
Now, let's calculate the change in potential energy:
ΔU = U2 - U1
ΔU = -0.5 • U1 - (-U1)
ΔU = -0.5 • U1 + U1
ΔU = 0.5 • U1
Finally, we can calculate the work done:
W = -ΔU
W = -0.5 • U1
Given that the magnetic moment of the bar magnet is 2×10^4 J T^-1 and the magnetic field is 6×10^-4 T, we can substitute these values into the equation:
W = -0.5 • (2×10^4 J T^-1) • (6×10^-4 T)
W = -0.5 • (2×10^4) • (6×10^-4) J
W = -6 J
Since work is a scalar quantity, the negative sign indicates that work is done by an external agent to change the orientation of the magnet.
Therefore, the correct answer is option B: 6 J.
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A bar magnet having a magnetic moment of 2×104JT−1 is free to rotate in a horizontal plane. A horizontal magnetic field B = 6×10−4T exists in the space. The work done in taking the magnet slowly from a direction parallel to the field to a direction 60° from the field isa)12 Jb)6 Jc)2 Jd)0.6 JCorrect answer is option 'B'. Can you explain this answer?
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A bar magnet having a magnetic moment of 2×104JT−1 is free to rotate in a horizontal plane. A horizontal magnetic field B = 6×10−4T exists in the space. The work done in taking the magnet slowly from a direction parallel to the field to a direction 60° from the field isa)12 Jb)6 Jc)2 Jd)0.6 JCorrect answer is option 'B'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A bar magnet having a magnetic moment of 2×104JT−1 is free to rotate in a horizontal plane. A horizontal magnetic field B = 6×10−4T exists in the space. The work done in taking the magnet slowly from a direction parallel to the field to a direction 60° from the field isa)12 Jb)6 Jc)2 Jd)0.6 JCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bar magnet having a magnetic moment of 2×104JT−1 is free to rotate in a horizontal plane. A horizontal magnetic field B = 6×10−4T exists in the space. The work done in taking the magnet slowly from a direction parallel to the field to a direction 60° from the field isa)12 Jb)6 Jc)2 Jd)0.6 JCorrect answer is option 'B'. Can you explain this answer?.
A bar magnet having a magnetic moment of 2×104JT−1 is free to rotate in a horizontal plane. A horizontal magnetic field B = 6×10−4T exists in the space. The work done in taking the magnet slowly from a direction parallel to the field to a direction 60° from the field isa)12 Jb)6 Jc)2 Jd)0.6 JCorrect answer is option 'B'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A bar magnet having a magnetic moment of 2×104JT−1 is free to rotate in a horizontal plane. A horizontal magnetic field B = 6×10−4T exists in the space. The work done in taking the magnet slowly from a direction parallel to the field to a direction 60° from the field isa)12 Jb)6 Jc)2 Jd)0.6 JCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bar magnet having a magnetic moment of 2×104JT−1 is free to rotate in a horizontal plane. A horizontal magnetic field B = 6×10−4T exists in the space. The work done in taking the magnet slowly from a direction parallel to the field to a direction 60° from the field isa)12 Jb)6 Jc)2 Jd)0.6 JCorrect answer is option 'B'. Can you explain this answer?.
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