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 cm` , `b = 100cm`.

Options

A. `0.23 mV`
B. `0.46 mV`
C. `0.16 mV`
D. `0.32m V`

Answer

B

Explanation

Let there be an an element `dx` of rod at a distance `x` from the wire.
emf developed in the element, `dE = Bdxv`
`:. dE = ((mu_(0))/(4pi)(2I)/(x))dx v`
`:. E = (mu_(0)Iv)/(2pi)int_(a)^(b)(dx)/(x) = (mu_(0)Iv)/(2pi)"log"_(e)(b)/(a)`
`:.E = (4pi xx 10^(-7) xx 100 xx 5)/(2pi) "log"_(e) (100)/(1)`
`= 4.6 xx 10^(-4) V = 0.46 mV`