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Using Lenz's Law

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Question

Figure shows a copper rod moving with velocity $v$ parallel to a long straight wire carrying current $= 100 A$ . Calculate the induced emf in the rod, where $v = 5 m s^{- 1}, a = 1 c m, b = 100 c m$ .

A

0.23 m V

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B

0.46 m V

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C

0.16 m V

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D

0.32 m V

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Solution

The correct option is D $0.46 m V$
$f o r c e o n a p a r t i c l e o f u n i t c h a r g e i s F = v B = v \frac{μ_{0} I}{2 π x} d W = F d x \Rightarrow d W = v \frac{μ_{0} I}{2 π x} d x \Rightarrow W = E M F = v \frac{μ_{0} I}{2 π} l n (\frac{b}{a}) = 5 \times \frac{μ_{0} \times 100}{2 π} n (\frac{100}{1}) = 0.46 m V$

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