# A rectangular loop of sides 10 cm and 5 cm carrying a current I of 12 A is placed in different orientations as shown in the figures below :If there is a uniform magnetic field of 0.3 T in the positive z direction, in which orientations the loop would be in (i) stable equilibrium and (ii) unstable equilibrium ? Option 1)  (a) and (b), respectively   Option 2)  (a) and (c), respectively Option 3)  (b) and (d), respectively   Option 4) (b) and (c), respectively

As we learnt in

Magnetic moment (M) -

M=NiA

- wherein

N-number of turns in the coil

i-current throughout the coil

A-area of the coil

$I=12A, \overrightarrow{B}=0.3 \hat{K}T, A=10\times ^{5} cm^{2}=50\times 10^{-4}m^{2}$

$\overrightarrow{M}=IA\hat{n}= 12\times 50\times 10^{-4}\hat{n}Am^{2}$

$\overrightarrow{M_{1}}=6\times 10^{-2} \hat{i}\, \, \, \,\, \, \, \, A-m^{2}\, \, \, \,\, \, \, \, \overrightarrow{{M_{2}}}=6\times 10^{-2} \hat{K} m^{2}\, \, \, \, \, \, \overrightarrow{{M_{3}}}=-6\times 10^{-2} JA \times m^{2}\, \, \, \overrightarrow{{M_{4}}}=-6\times 10^{-2} \hat{K}A-m^{2}$

In the figure (b) since magnetic field and magnetic moment are parallel to each other and hence energy is minimum. This system is stable equilibrium

In the figure (d) since magnetic field and magnetic moment are antiparallel to each other and hence energy is maximum. This system is unstable equilibrium

Option 1)

(a) and (b), respectively

Incorrect Option

Option 2)

(a) and (c), respectively

Incorrect Option

Option 3)

(b) and (d), respectively

Correct Option

Option 4)

(b) and (c), respectively

Incorrect Option

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