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Work done in rotating a bar magnet from ...

Work done in rotating a bar magnet from 0 to angle `theta` is:

A

`MH(1-cos theta)`

B

`M/H(1- cos theta)`

C

`M/H (cos theta -1)`

D

`MH(cos theta -1)`

Text Solution

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The correct Answer is:
To find the work done in rotating a bar magnet from an angle of 0 degrees to an angle of θ, we can follow these steps: ### Step-by-Step Solution: 1. **Understand the Formula**: The work done (W) in rotating a bar magnet is given by the formula: \[ W = M B (\cos \theta_i - \cos \theta_f) \] where: - \( M \) is the magnetic moment of the bar magnet, - \( B \) is the magnetic field strength, - \( \theta_i \) is the initial angle, - \( \theta_f \) is the final angle. 2. **Identify Initial and Final Angles**: In this case, we are rotating the magnet from: - Initial angle \( \theta_i = 0^\circ \) - Final angle \( \theta_f = \theta \) 3. **Substitute the Angles into the Formula**: Plugging the angles into the work done formula gives: \[ W = M B (\cos 0^\circ - \cos \theta) \] 4. **Calculate Cosine Values**: We know that: - \( \cos 0^\circ = 1 \) Therefore, the equation simplifies to: \[ W = M B (1 - \cos \theta) \] 5. **Final Expression for Work Done**: Thus, the work done in rotating the bar magnet from 0 degrees to θ degrees is: \[ W = M B (1 - \cos \theta) \] ### Final Answer: The work done in rotating a bar magnet from 0 to angle θ is: \[ W = M B (1 - \cos \theta) \]

To find the work done in rotating a bar magnet from an angle of 0 degrees to an angle of θ, we can follow these steps: ### Step-by-Step Solution: 1. **Understand the Formula**: The work done (W) in rotating a bar magnet is given by the formula: \[ W = M B (\cos \theta_i - \cos \theta_f) \] ...
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Knowledge Check

  • If a bar magnet of magnetic moment 'm' is freely suspended in a uniform magnetic field B, the work done in rotating the magnet through an angle thete is

    A
    `mB(1- sin theta)`
    B
    `mB sin theta`
    C
    `mB cos B`
    D
    `mB(1-costheta)`
  • If a bar magnet of magnetic moment M is freely suspended in a uniform magnetic field of strength B , the work done in rotating the magnet through an "angle"theta is

    A
    `MB(1-sintheta)`
    B
    `MBsintheta`
    C
    `MBcostheta`
    D
    `MB(1-costheta)`
  • The work done in rotating a bar magnet f magnetic moment M from its unstable equilibrium positon to its stable equilibrium position in a uniform magnetic field B is

    A
    `2MB`
    B
    `MB`
    C
    `-MB`
    D
    `-2MB`
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