(B) The work done $W$ in rotating a magnetic dipole in a uniform magnetic field $B$ from an angle $\theta_1$ to $\theta_2$ is given by $W = MB(\cos \t

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(B) The work done $W$ in rotating a magnetic dipole in a uniform magnetic field $B$ from an angle $\theta_1$ to $\theta_2$ is given by $W = MB(\cos \theta_1 - \cos \theta_2)$.Assuming the initial position is the stable equilibrium position,$\theta_1 = 0^{\circ}$.For the first case,$\theta_2 = 90^{\circ}$:$W_1 = MB(\cos 0^{\circ} - \cos 90^{\circ}) = MB(1 - 0) = MB$.For the second case,$\theta_2 = 60^{\circ}$:$W_2 = MB(\cos 0^{\circ} - \cos 60^{\circ}) = MB(1 - 0.5) = 0.5MB$.According to the problem,$W_1 = n \times W_2$.Substituting the values: $MB = n \times (0.5MB)$.$1 = n \times 0.5$.$n = 1 / 0.5 = 2$.

Class 12 Physics Magnetism and Matter Magnetic field due to magnetic dipole and Dipole in Magnetic Field and Poential Energy and Work Done

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The work done in turning a magnet of magnetic moment $M$ by an angle of $90^{\circ}$ from the magnetic meridian is $n$ times the corresponding work done to turn it through an angle of $60^{\circ}$. Find the value of $n$ (given $\cos 90^{\circ} = 0, \cos 60^{\circ} = 0.5$).

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A
$0.5$
B
$2$
C
$0.25$
D
$1$

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Magnetic field due to magnetic dipole and Dipole in Magnetic Field and Poential Energy and Work Done

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The work done in turning a magnet of magnetic moment $M$ by an angle of $90^{\circ}$ from the magnetic meridian is $n$ times the corresponding work done to turn it through an angle of $60^{\circ}$. Find the value of $n$ (given $\cos 90^{\circ} = 0, \cos 60^{\circ} = 0.5$).

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$A$ short bar magnet placed with its axis at $30^{\circ}$ to a uniform external magnetic field of $0.5 \ T$ experiences a torque of magnitude equal to $4.5 \times 10^{-2} \ J$. The magnitude of the magnetic moment is . . . . . . .

$A$ small bar magnet of magnetic moment $M$ is placed in a uniform magnetic field $H$. If the magnet makes an angle of $30^{\circ}$ with the field,the torque acting on the magnet is:

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$A$ negative charge is given to a nonconducting loop and the loop is rotated in the plane of paper about its centre as shown in the figure. The magnetic field produced by the ring affects a small magnet placed above the ring in the same plane:

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