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A current loop in a magnetic field [NEET 2013]
- a)can be in equilibrium in one orientation
- b)can be in equilibrium in two orientations,both the equilibrium states are unstable
- c)can be in equilibrium in two orientations,one stable while the other is unstable
- d)experiences a torque whether the field isuniform or non-uniform in all orientations
Correct answer is option 'C'. Can you explain this answer?
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A current loop in a magnetic field [NEET 2013]a)can be in equilibrium ...
A current loop in a magnetic field is in equilibrium in two orientations one is stable and another unstable.
= M B sinθ
Do not experience a torque in some orientations Hence option (c) is correct.
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A current loop in a magnetic field [NEET 2013]a)can be in equilibrium ...
Understanding the Current Loop in a Magnetic Field
A current loop placed in a magnetic field experiences torque, which influences its orientation. The analysis of equilibrium states is crucial for understanding this behavior.
Equilibrium States of the Current Loop
- When a current loop is placed in a magnetic field, it can achieve equilibrium in two distinct orientations:
- Stable Equilibrium: This occurs when the magnetic moment of the loop is aligned with the magnetic field direction. In this position, any slight displacement will result in a restoring torque that brings the loop back to equilibrium.
- Unstable Equilibrium: This occurs when the magnetic moment is aligned opposite to the magnetic field direction. In this configuration, any small displacement will result in a torque that further moves the loop away from this position, making it unstable.
Torque in Uniform and Non-Uniform Fields
- Regardless of whether the magnetic field is uniform or non-uniform, the current loop experiences torque in all orientations:
- Uniform Magnetic Field: The torque is given by the formula \( \tau = \vec{m} \times \vec{B} \), where \( \vec{m} \) is the magnetic moment, and \( \vec{B} \) is the magnetic field. This torque tends to align the loop with the field.
- Non-Uniform Magnetic Field: The loop can experience forces in addition to torque, but it will still have a tendency to rotate towards an equilibrium orientation.
Conclusion
Thus, the correct answer is option 'C': a current loop can be in equilibrium in two orientations, one stable while the other is unstable. Understanding the stability of these orientations helps in predicting the behavior of loops in magnetic fields, which is fundamental in electromagnetism.
A current loop placed in a magnetic field experiences torque, which influences its orientation. The analysis of equilibrium states is crucial for understanding this behavior.
Equilibrium States of the Current Loop
- When a current loop is placed in a magnetic field, it can achieve equilibrium in two distinct orientations:
- Stable Equilibrium: This occurs when the magnetic moment of the loop is aligned with the magnetic field direction. In this position, any slight displacement will result in a restoring torque that brings the loop back to equilibrium.
- Unstable Equilibrium: This occurs when the magnetic moment is aligned opposite to the magnetic field direction. In this configuration, any small displacement will result in a torque that further moves the loop away from this position, making it unstable.
Torque in Uniform and Non-Uniform Fields
- Regardless of whether the magnetic field is uniform or non-uniform, the current loop experiences torque in all orientations:
- Uniform Magnetic Field: The torque is given by the formula \( \tau = \vec{m} \times \vec{B} \), where \( \vec{m} \) is the magnetic moment, and \( \vec{B} \) is the magnetic field. This torque tends to align the loop with the field.
- Non-Uniform Magnetic Field: The loop can experience forces in addition to torque, but it will still have a tendency to rotate towards an equilibrium orientation.
Conclusion
Thus, the correct answer is option 'C': a current loop can be in equilibrium in two orientations, one stable while the other is unstable. Understanding the stability of these orientations helps in predicting the behavior of loops in magnetic fields, which is fundamental in electromagnetism.
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A current loop in a magnetic field [NEET 2013]a)can be in equilibrium in one orientationb)can be in equilibrium in two orientations,both the equilibrium states are unstablec)can be in equilibrium in two orientations,one stable while the other is unstabled)experiences a torque whether the field isuniform or non-uniform in all orientationsCorrect answer is option 'C'. Can you explain this answer?
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