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

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

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.PhysicsNCERTStandard XII

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