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A rectangular coil ABCD is hung from one...

A rectangular coil ABCD is hung from one side of a balance as shown in higure. A 500 g mass is added to the other arm to balance the weight of the coil. A current of 9.8 A is passed through the coil and a constant magnetic field of 0.4 T acting inward (in xz plane) is switched on such that only arm CD of length 1.5 cm lies in the field. The additional mass m must be added to regain the balance is

Text Solution

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For equilibrium/balance, net torque should also be equal to zero
When the field is off `sumt=0` considering the separation of each hung from mid-point be l
`Mgl=W_("coil")l`
`500gl=W_("coil")l`
`W_("coil")=500xx9.8N`
Taking moment of force about mid-point, we have the weight of coil
When the magnetic field is switched on
`Mgl+mgl=W_("coil")l+IBL sin90^(@)I`
`mgl=BILl`
`m=(BIL)/(g)=(0.2xx4.9xx1xx10^(-2))/(9.8)=10^(-3)kg=1g`
Thus, 1 g of additional mass must be added tor eagin the balance.
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