There are two wires ab and cd in a vertical plane as shown in figure. Direction of current in wire ab is rightwards. Choose the correct statement among the given options.

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Equilibrium of wire cd will be stable equilibrium.

Equilibrium of wire ab will be stable equilibrium.

If wire ab is fixed, then wire cd can be kept in equilibrium by the current in cd in leftward direction.

If wire cd is fixed, then wire ab can be kept in equilibrium by flowing current cd in rightward direction.

answer is A, B, C.

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Detailed Solution

Direction of magnetic field produced by ab at the site of cd is into the plane of figure .

Magnetic force on wire cd is $\vec{F} = i \vec{l} \times \vec{B} a n d \vec{F} i s v e r t i c a l l y u p w a r d .$

If cd is slightly pushed vertically downward , $\vec{F} i n c r e a s e s a n d a f t e r r e l e a s e c d w i l l b e p u s h e d b a c k t o i t s o r i g i n a l p o s i t i o n .$

If cd is slightly pulled upward , $\vec{F} w i l l d e c r e a s e a n d t h e w i r e w i l l b e b r o u g h t b a c k t o i t s o r i g i n a l p o s i t i o n b y g r a v i t y .$ So the equilibrium is stable equilibrium .

Direction of magnetic field produced by cd at the location of ab is inward.So the magnetic force on ab is vertically upward which can balance the weight of ab. If ab is slightly pushed down , $\vec{F}$

will decrease and after release ab will further move down due to gravity. So the equilibrium is unstable .

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