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A: A magnetic dipole experiences maximum...

A: A magnetic dipole experiences maximum torque when it is placed normal to the magnetic field.
R: The minimum potential energy of magnetic dipole is zero.

A

If both Assertion & Reason are true and the reason is the correct explanation of the assertion then mark (1)

B

If both Assertion & Reason are true but the reason is not the correct explanation of the assertion, then mark 2.

C

If assertion is true statement but Reason is false, then mark (3)

D

If both Assertion and Reason are false statements, then mark (4)

Text Solution

AI Generated Solution

The correct Answer is:
To solve the assertion and reason question, we will analyze both statements step by step. ### Step 1: Analyze the Assertion The assertion states: "A magnetic dipole experiences maximum torque when it is placed normal to the magnetic field." - The torque (\( \tau \)) experienced by a magnetic dipole in a magnetic field is given by the formula: \[ \tau = \mathbf{m} \times \mathbf{B} = mB \sin \theta \] where: - \( \mathbf{m} \) is the magnetic dipole moment, - \( \mathbf{B} \) is the magnetic field, - \( \theta \) is the angle between \( \mathbf{m} \) and \( \mathbf{B} \). - For torque to be maximum, \( \sin \theta \) must be maximum, which occurs when \( \theta = 90^\circ \). At this angle, the magnetic dipole is placed normal (perpendicular) to the magnetic field. **Conclusion for Assertion**: The assertion is true. ### Step 2: Analyze the Reason The reason states: "The minimum potential energy of a magnetic dipole is zero." - The potential energy (\( U \)) of a magnetic dipole in a magnetic field is given by the formula: \[ U = -\mathbf{m} \cdot \mathbf{B} = -mB \cos \theta \] - To find the minimum potential energy, we need to analyze the cosine function: - When \( \theta = 0^\circ \) (dipole aligned with the field), \( U = -mB \). - When \( \theta = 90^\circ \) (dipole normal to the field), \( U = 0 \). - When \( \theta = 180^\circ \) (dipole anti-aligned with the field), \( U = mB \). - The minimum potential energy occurs when \( \theta = 0^\circ \) and is equal to \( -mB \), which is not zero. **Conclusion for Reason**: The reason is false. ### Final Conclusion - The assertion is true, and the reason is false. Therefore, the correct answer is that the assertion is true, but the reason is false.
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