Question

state orientation of magnetic dipole with respect to magnetic field which posses maximum magnetic potential energy​

Answer 1

Answer:

Potential energy of a magnetic dipole in a uniform magnetic field U=−MBcosq clearly the potential energy is maximum when cosθ=−1 or θ=π That is, potential energy is maximum when magnetic dipole with its magnetic moment M is oriented opposite to the direction of magnetic field ( or angle between M and δ is 180o).

Explanation:

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Answer 2

ORIENTATION OF MAGNETIC DIPOLE:

For max potential energy :

• Lets assume that magnetic dipole was experiencing a torque of $\tau$.

• Let potential energy be U :

$\therefore \:\Delta U = W$

$\displaystyle \implies \:\Delta U = \int \tau \: d \theta$

$\displaystyle \implies \:\Delta U = \int_{ \theta1}^{ \theta2} \tau \: d \theta$

$\displaystyle \implies \:\Delta U = \int_{ \theta1}^{ \theta2} MB \sin( \theta) \: d \theta$

$\displaystyle \implies \:\Delta U = MB \int_{ \theta1}^{ \theta2} \sin( \theta) \: d \theta$

$\displaystyle \implies \:\Delta U = - MB\cos( \theta) \bigg| _{ \theta1}^{ \theta2}$

$\displaystyle \implies \:\Delta U = MB\cos( \theta) \bigg| _{ \theta2}^{ \theta1}$

$\displaystyle \implies \: \Delta U = MB \bigg \{\cos( \theta1) - \cos( \theta2) \bigg \}$

From here, we can understand that :

• At any specific angle , the potential energy will be :

$\displaystyle \implies \: U = - MB \cos( \theta)$

$\displaystyle \implies \: U_{max} = - MB \cos( {180}^{ \circ} )$

$\displaystyle \implies \: U_{max} = MB$

So, dipole has to be placed opposite to magnetic field intensity (at 180°).