Question

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

• A. $4g$
• B. $5g$
• C. $6g$
• D. $7g$

Answer 1

The correct option is C $6g$

In absence of magnetic field the weight added in one pan balances the rectangular coil in the other pan of balance,

$\therefore Mgl=W_{coil}l$ or $W_{coil}=Mg=0.5\times 9.8N$

When current I is passed through the coil and the magnetic field is switched on.

Let m mass be added in the first pan to regain the balance

Then $Mgl+mgl=W_{coil}l+IBLsin{90}^{o}l$

$mgl=IBLl$

or $m=\frac{IBL}{g}=\frac{9.8\times 0.4\times 1.5\times {10}^{-2}}{9.8}=0.6\times {10}^{-2}kg$

$=6\times {10}^{-3}kg=6g$