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. (a) `0.23mV`
B. (b) `0.46mV`
C. ( c) `0.16mV`
D. (d) `0.32mV`

Answer

B

Explanation

(b) Let there be an element, `dE = B dx v`
`:.` `dE = ((mu_(0))/(4pi)(2I)/(x))dxv`
`:.` `(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))`