# A copper rod moves with a constant angular velocity ω, about a long straight wire carrying a current i. If the ends of the rod from the wire are at distances a and b, then the e.m.f. induced in the rod is Option 1) $\frac{\mu 0i\left ( wa \right )}{2\pi} In\frac{b}{a}$ Option 2) $\frac{\mu 0i\left ( wb \right )}{2\pi} In\frac{b}{a}$ Option 3) zero Option 4) $\frac{\mu 0iw\left ( a+b\right )}{2\pi} In\frac{b}{a}$

Motional EMF -

$\varepsilon = Blv$

- wherein

$B\rightarrow$ magnetic field

$l\rightarrow$ length

$u\rightarrow$ velocity of u perpendicular to uniform magnetic field.

The velocity of any element and field applied by current carrying wire are parallel. Hence Emf induced is Zero.

Option 1)

$\frac{\mu 0i\left ( wa \right )}{2\pi} In\frac{b}{a}$

Option is incorrect

Option 2)

$\frac{\mu 0i\left ( wb \right )}{2\pi} In\frac{b}{a}$

Option is incorrect

Option 3)

zero

Option is correct

Option 4)

$\frac{\mu 0iw\left ( a+b\right )}{2\pi} In\frac{b}{a}$

Option is incorrect

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