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Question

A rectangular coil of conductor ABCD with the length $$AD=3\ $$ and breadth $$DC=2\ m $$is hung from one of the arms of a balance, as shown in the Figure. A current $$I=8\ A$$ is passed through the coil. When the magnetic Field turned off, a  mass M kg is added to the pan of other arm to balance the coil. When the magnetic field of strength $$0.4\ T$$ is switched on then, the system is

44458_82566539633445b8899347c49c4aaf8a.jpg


A
in equilibrium by taking a mass of 0.32 kg from left pan.
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B
in equilibrium by adding a mass of 0.64 kg to the left pan.
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C
in equilibrium by reversing the current and taking a mass of 0.64kg from the left pan.
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D
in equilibrium by reversing the current and adding a mass of 0.32kg to the left pan.
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Solution

The correct options are
B in equilibrium by adding a mass of 0.64 kg to the left pan.
C in equilibrium by reversing the current and taking a mass of 0.64kg from the left pan.
When the magnetic field is switched off, for equilibrium, if W is the weight of the coil, then, net torque acting about O should be zero.
When the field is switched on, the force on CD$$=ILB$$ downward. Hence to balance, mass m should be added to the left pan, such that,
$$mg=ILB$$ or $$m=\dfrac{ILB}{g}$$
$$\therefore m=\dfrac{8\times 2\times 0.4}{10}=0.64kg$$
By reversing the current, a mass of 0.64kg should be taken from the left pan.

Physics
NCERT
Standard XII

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