Question 96 of 153

A $10m$ long horizontal wire extends from North East to South West. It is falling with a speed of $5.0m{s}^{-1},$ at right angles to the horizontal component of the earth's magnetic field of $0.3\times {10}^{-4}Wb{m}^{-2}.$ The value of the induced emf in the wire is:

A$0.3\times {10}^{-3}V$B$1.1\times {10}^{-3}V$C$2.5\times {10}^{-3}V$D$1.5\times {10}^{-3}V$

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Answer: (B) $1.1\times {10}^{-3}V$

The wire makes an angle $45^{\circ}$ with the magnetic field lines. Therefore, the induced emf will be,
$\epsilon =Bvl\sin {45}^{0}$
$=0.3\times {10}^{-4}\times 5\times 10\times \dfrac{1}{\sqrt{2}}$
$=1.1\times {10}^{-3}V$