The circuit in figure consists of wires at the top and bottom and identical springs as the left and right sides. The wire at the bottom has a mass of $10\, g$ and is $5\, cm$ long. The wire is hanging as shown in the figure. The springs stretch $0.5\, cm$ under the weight of the wire and the circuit has a total resistance of $12\, \Omega $. When the lower wire is subjected to a static magnetic field, the springs, stretch an additional $0.3\, cm$. The magnetic field is
AIEEE 2012, Diffcult
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$I = \frac{\varepsilon }{R} = \frac{{24}}{{12}} = 2\,A$
Magnetic force$=Il B \sin \left(\frac{\pi}{2}\right)=2 \times 5 \times 10^{-2} \times B=\frac{B}{10}$
$2 k x_{1}=m g, 2 k=\frac{m g}{x_{1}}$ and
$2 k\left(x_{1}+x_{2}\right)=m g+I l B$
$2 k x_{1}+2 k x_{2}=m g+I l B$
$\frac{m g}{x_{1}} x_{2}=Il B$
$10 \times 10^{-3} \times 10 \times \frac{0.3}{0.5}=\frac{B}{10} \Rightarrow B=600 \times 10^{-3}=0.6 \,T$
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