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Standard XII

Physics

EMF and EMF Devices

A sliding wir...

Question

A sliding wire of length $0.25 m$ and having a resistance of $0.5 Ω$ moves along conducting guiding rails $AB$ and $CD$ with a uniform speed of $4 {ms}^{- 1}$ . A magnetic field of $0.5 T$ exists normal to the plane of $ABCD$ directed into the page. The guiding rails are short-circuited with resistances of $4 Ω$ and $2 Ω$ as shown. The current through the sliding wire is

0.72 A

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0.37 A

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0.27 A

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1.0 A

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Solution

The correct option is C $0.27 A$

When a conductor moves in a magnetic field, then motional emf induced is given by , $e = B l v$

(Where $B, l$ and $v$ are mutually perpendicular to each other)

Induced EMF, $e = 0.5 \times 0.25 \times 4 = 0.5 V$

Induced current, $i = \frac{e}{R^{'}} = \frac{e}{\frac{R_{1} R_{2}}{R_{1} + R_{2}} + r}$

Substituting the data given in the question,

$i = \frac{0.5}{\frac{4 \times 2}{4 + 2} + 0.5} = \frac{0.5 \times 6}{8 + 3} = \frac{3}{11} = 0.27 A$

Hence, option (c) is the correct answer.

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