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A bar magnet of pole strength 2 A-m is kept in a magnetic field of induction 4 x 10−5 wbm−2 such that the axis of the magnet makes an angle 30º with the direction of the field. The couple acting on the magnet is found to be 80 10−7N-m . Then the distance between the poles of the magnet is
- a)20m
- b)2m
- c)3cm
- d)20cm
Correct answer is option 'D'. Can you explain this answer?
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A bar magnet of pole strength 2 A-m is kept in a magnetic field of ind...
Understanding the Problem
To find the distance between the poles of the bar magnet, we need to use the formula for the couple acting on a magnetic dipole in a magnetic field.
Given Data
- Pole strength, \( m = 2 \, \text{A-m} \)
- Magnetic field induction, \( B = 4 \times 10^{-5} \, \text{wbm}^{-2} \)
- Angle, \( \theta = 30^\circ \)
- Couple, \( \tau = 80 \times 10^{-7} \, \text{N-m} \)
Formula for the Couple
The couple \( \tau \) acting on a magnetic dipole is given by the formula:
\[
\tau = m \cdot B \cdot \sin(\theta)
\]
Where:
- \( m \) is the pole strength,
- \( B \) is the magnetic field induction,
- \( \theta \) is the angle between the magnet and the magnetic field.
Calculating the Couple
Substituting the known values into the formula:
\[
80 \times 10^{-7} = 2 \cdot (4 \times 10^{-5}) \cdot \sin(30^\circ)
\]
Since \( \sin(30^\circ) = \frac{1}{2} \):
\[
80 \times 10^{-7} = 2 \cdot (4 \times 10^{-5}) \cdot \frac{1}{2}
\]
This simplifies to:
\[
80 \times 10^{-7} = 4 \times 10^{-5}
\]
Finding the Distance Between the Poles
We know that the magnetic moment \( m \) can also be expressed in terms of the distance \( d \) between the poles as:
\[
m = \frac{p \cdot d}{2}
\]
Where \( p \) is the pole strength. Rearranging gives:
\[
d = \frac{2m}{p}
\]
Substituting \( m = 2 \) and \( p = 4 \times 10^{-5} \):
\[
d = \frac{2 \cdot 2}{4 \times 10^{-5}} = 20 \, \text{cm}
\]
Conclusion
The distance between the poles of the magnet is 20 cm, making option 'D' the correct answer.
To find the distance between the poles of the bar magnet, we need to use the formula for the couple acting on a magnetic dipole in a magnetic field.
Given Data
- Pole strength, \( m = 2 \, \text{A-m} \)
- Magnetic field induction, \( B = 4 \times 10^{-5} \, \text{wbm}^{-2} \)
- Angle, \( \theta = 30^\circ \)
- Couple, \( \tau = 80 \times 10^{-7} \, \text{N-m} \)
Formula for the Couple
The couple \( \tau \) acting on a magnetic dipole is given by the formula:
\[
\tau = m \cdot B \cdot \sin(\theta)
\]
Where:
- \( m \) is the pole strength,
- \( B \) is the magnetic field induction,
- \( \theta \) is the angle between the magnet and the magnetic field.
Calculating the Couple
Substituting the known values into the formula:
\[
80 \times 10^{-7} = 2 \cdot (4 \times 10^{-5}) \cdot \sin(30^\circ)
\]
Since \( \sin(30^\circ) = \frac{1}{2} \):
\[
80 \times 10^{-7} = 2 \cdot (4 \times 10^{-5}) \cdot \frac{1}{2}
\]
This simplifies to:
\[
80 \times 10^{-7} = 4 \times 10^{-5}
\]
Finding the Distance Between the Poles
We know that the magnetic moment \( m \) can also be expressed in terms of the distance \( d \) between the poles as:
\[
m = \frac{p \cdot d}{2}
\]
Where \( p \) is the pole strength. Rearranging gives:
\[
d = \frac{2m}{p}
\]
Substituting \( m = 2 \) and \( p = 4 \times 10^{-5} \):
\[
d = \frac{2 \cdot 2}{4 \times 10^{-5}} = 20 \, \text{cm}
\]
Conclusion
The distance between the poles of the magnet is 20 cm, making option 'D' the correct answer.
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A bar magnet of pole strength 2 A-m is kept in a magnetic field of induction 4 x 10−5 wbm−2 such that the axis of the magnet makes an angle 30º with the direction of the field. The couple acting on the magnet is found to be 80 10−7N-m . Then the distance between the poles of the magnet isa)20mb)2mc)3cmd)20cmCorrect answer is option 'D'. Can you explain this answer?
Question Description
A bar magnet of pole strength 2 A-m is kept in a magnetic field of induction 4 x 10−5 wbm−2 such that the axis of the magnet makes an angle 30º with the direction of the field. The couple acting on the magnet is found to be 80 10−7N-m . Then the distance between the poles of the magnet isa)20mb)2mc)3cmd)20cmCorrect answer is option 'D'. 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 of pole strength 2 A-m is kept in a magnetic field of induction 4 x 10−5 wbm−2 such that the axis of the magnet makes an angle 30º with the direction of the field. The couple acting on the magnet is found to be 80 10−7N-m . Then the distance between the poles of the magnet isa)20mb)2mc)3cmd)20cmCorrect answer is option 'D'. 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 of pole strength 2 A-m is kept in a magnetic field of induction 4 x 10−5 wbm−2 such that the axis of the magnet makes an angle 30º with the direction of the field. The couple acting on the magnet is found to be 80 10−7N-m . Then the distance between the poles of the magnet isa)20mb)2mc)3cmd)20cmCorrect answer is option 'D'. Can you explain this answer?.
A bar magnet of pole strength 2 A-m is kept in a magnetic field of induction 4 x 10−5 wbm−2 such that the axis of the magnet makes an angle 30º with the direction of the field. The couple acting on the magnet is found to be 80 10−7N-m . Then the distance between the poles of the magnet isa)20mb)2mc)3cmd)20cmCorrect answer is option 'D'. 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 of pole strength 2 A-m is kept in a magnetic field of induction 4 x 10−5 wbm−2 such that the axis of the magnet makes an angle 30º with the direction of the field. The couple acting on the magnet is found to be 80 10−7N-m . Then the distance between the poles of the magnet isa)20mb)2mc)3cmd)20cmCorrect answer is option 'D'. 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 of pole strength 2 A-m is kept in a magnetic field of induction 4 x 10−5 wbm−2 such that the axis of the magnet makes an angle 30º with the direction of the field. The couple acting on the magnet is found to be 80 10−7N-m . Then the distance between the poles of the magnet isa)20mb)2mc)3cmd)20cmCorrect answer is option 'D'. Can you explain this answer?.
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