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Magnetism And Matter — Physics STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 SciencePhysicsMagnetism And Matter4 Marks
Question
Deduce the expression for the torque $\overrightarrow{\tau}$ acting on a planar loop of area $\overrightarrow{\text{A}}$ and carrying current I placed in a uniform magnetic field $\overrightarrow{\text{B}}.$ If the loop is free to rotate, what would be its orientation in stable equilibrium?
✓

Answer



Force on each perpendicular arm:
$?_1 = ?_2 = ?\ ?\ ?$
Moment of couple = ? ? ?. ? sin ?
$? = ?\ ??\ ?\ ????$
? = I ?? ???? $\overrightarrow{\tau} =\overrightarrow{\text{IA}}\times\overrightarrow{\text{B}}$
When the plane of the loop is perpendicular to the magnetic field, the loop will be in stable equilibrium.$(\overrightarrow{\text{A}}||\overrightarrow{\text{B}}) , \Rightarrow\theta = 0^{\circ}$
$\overrightarrow{\text{M}} = $ Equivalent magnetic moment of the planer loop $ = \overrightarrow{\text{IA}}$
$\therefore \text{Torque} =\overrightarrow{\text{M}}\times\overrightarrow{\text{B}} = \overrightarrow{\text{IA}}\times\overrightarrow{\text{B}}$
$\text{|??????|} = \text{IAB}\sin\theta$.

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